I am using Maple 2020.2 and it seems that the Linear Algebra package is incompatable with the Vector Calculus package:

Why not a friendly error message?
I want to use the Jacobian and the Hessian. Are there alternatives? MTM package can give a Jacobian, but no Hessian (but MTM is also tricky to use).

Harry

I want to compute the Lie derivative of a large expression in maple.
The expression is attached, there are 20 vars in total. But Maple cannot do that (after 7hrs of working!), but this is doable with another math tool which first turns the expression into subexpressions.
However, I want to do this in Maple.
I have already tried to simplify/combine/factor/use the Lie algebra package, none of them helped.
Any suggestion is highly appreciated

(6*m__1*(2*x[13]*x[12]*((x[12]*(cos(x[7])^2 - 2)*(x[17] - g__1)*cos(x[8])^2 - 2*x[12]*(x[17] - g__1)*cos(x[7])^2 + x[18]*cos(x[7])*sin(x[7])*sin(x[8]) + x[12]*(x[17] - g__1))*cos(x[6])^2 - 2*cos(x[8])*(x[12]*sin(x[8])*(x[17] - g__1)*sin(x[7]) + x[18]*cos(x[7])/2)*sin(x[6])*cos(x[6]) + x[12]*cos(x[8])^2*(x[17] - g__1))*cos(x[4])^5 + ((-x[12]*x[13]*x[18]*sin(x[4])*(cos(x[7])^2 - 2)*cos(x[8])^2 + (((x[17] - g__1)*x[12]^2 + (2*x[17] - 2*g__1)*x[13]^2 - x[19])*x[12]*sin(x[8])*cos(x[7])^2 - 3*(x[12]^2*x[18] - (2*x[20])/9)*sin(x[7])*cos(x[7])/2 - 2*((x[17] - g__1)*x[12]^2 + (2*x[17] - 2*g__1)*x[13]^2 - x[19])*x[12]*sin(x[8]))*cos(x[8]) + 4*(x[18]*cos(x[7])^2/2 + x[12]*sin(x[7])*sin(x[8])*(x[17] - g__1)*cos(x[7]) - x[18]/4)*sin(x[4])*x[13]*x[12])*cos(x[6])^2 + (2*((x[17] - g__1)*x[12]^2 + (2*x[17] - 2*g__1)*x[13]^2 - x[19])*sin(x[7])*x[12]*sin(x[6])*cos(x[8])^2 - 4*(x[12]*x[13]*sin(x[4])*sin(x[6])*(x[17] - g__1)*cos(x[7]) - x[13]*x[18]*sin(x[4])*sin(x[6])*sin(x[7])*sin(x[8])/2 - x[12]*x[15]*(x[17] - g__1)/24)*x[12]*cos(x[8]) - (3*(x[12]^2*x[18] - (2*x[20])/9)*sin(x[8])*cos(x[7])/2 + ((x[17] - g__1)*x[12]^2 + (2*x[17] - 2*g__1)*x[13]^2 - x[19])*sin(x[7])*x[12])*sin(x[6]))*cos(x[6]) + x[12]*(-x[13]*x[18]*cos(x[8])^2*sin(x[4]) + ((x[17] - g__1)*x[12]^2 + (2*x[17] - 2*g__1)*x[13]^2 - x[19])*sin(x[8])*cos(x[8]) + x[12]*sin(x[8])*(x[17] - g__1)*(sin(x[6])*sin(x[7])*x[15] + x[14]*cos(x[7]))/6))*cos(x[4])^4 + ((-5*x[12]^2*x[13]*(cos(x[7])^2 - 2)*(x[17] - g__1)*cos(x[8])^2 - sin(x[4])*(3*(x[12]^2*x[18] - (2*x[20])/9)*sin(x[8])*cos(x[7])^2/2 + ((x[17] - g__1)*x[12]^2 + (2*x[17] - 2*g__1)*x[13]^2 - x[19])*sin(x[7])*x[12]*cos(x[7]) - 3*(x[12]^2*x[18] - (2*x[20])/9)*sin(x[8]))*cos(x[8]) + 7*(x[12]*(x[17] - g__1)*cos(x[7])^2 - (2*x[18]*cos(x[7])*sin(x[7])*sin(x[8]))/7 - (5*x[12]*(x[17] - g__1))/7)*x[13]*x[12])*cos(x[6])^2 - (3*sin(x[4])*(x[12]^2*x[18] - (2*x[20])/9)*sin(x[7])*cos(x[8])^2 - 10*(x[18]*cos(x[7])/5 + x[12]*sin(x[8])*(x[17] - g__1)*sin(x[7]))*x[13]*x[12]*cos(x[8]) + sin(x[4])*(((x[17] - g__1)*x[12]^2 + (2*x[17] - 2*g__1)*x[13]^2 - x[19])*x[12]*sin(x[8])*cos(x[7]) - 3*(x[12]^2*x[18] - (2*x[20])/9)*sin(x[7])/2))*sin(x[6])*cos(x[6]) - 5*x[12]^2*x[13]*(x[17] - g__1)*cos(x[8])^2 - (3*sin(x[4])*(x[12]^2*x[18] - (2*x[20])/9)*sin(x[8])*cos(x[8]))/2 + (x[17] - g__1)*(x[15]*cos(x[7])*sin(x[4])*sin(x[6])/6 - x[14]*sin(x[4])*sin(x[7])/6 + x[13])*x[12]^2)*cos(x[4])^3 - (7*x[12]*((-(4*x[13]*x[18]*sin(x[4])*(cos(x[7])^2 - 2)*cos(x[8])^2)/7 + (((x[17] - g__1)*x[12]^2 + ((4*x[17])/7 - (4*g__1)/7)*x[13]^2 - (2*x[19])/7)*sin(x[8])*cos(x[7])^2 - (5*x[12]*x[18]*cos(x[7])*sin(x[7]))/7 - 2*((x[17] - g__1)*x[12]^2 + ((4*x[17])/7 - (4*g__1)/7)*x[13]^2 - (2*x[19])/7)*sin(x[8]))*cos(x[8]) + 10*(x[18]*cos(x[7])^2/5 + x[12]*sin(x[7])*sin(x[8])*(x[17] - g__1)*cos(x[7]) - (2*x[18])/5)*sin(x[4])*x[13]/7)*cos(x[6])^2 + (2*((x[17] - g__1)*x[12]^2 + ((4*x[17])/7 - (4*g__1)/7)*x[13]^2 - (2*x[19])/7)*sin(x[7])*sin(x[6])*cos(x[8])^2 + (-(10*x[12]*x[13]*sin(x[4])*sin(x[6])*(x[17] - g__1)*cos(x[7]))/7 + (8*x[13]*x[18]*sin(x[4])*sin(x[6])*sin(x[7])*sin(x[8]))/7 + x[12]*x[15]*(x[17] - g__1)/21)*cos(x[8]) - ((5*x[12]*x[18]*cos(x[7])*sin(x[8]))/7 + ((x[17] - g__1)*x[12]^2 + ((4*x[17])/7 - (4*g__1)/7)*x[13]^2 - (2*x[19])/7)*sin(x[7]))*sin(x[6]))*cos(x[6]) - (4*x[13]*x[18]*cos(x[8])^2*sin(x[4]))/7 + ((x[17] - g__1)*x[12]^2 + ((4*x[17])/7 - (4*g__1)/7)*x[13]^2 - (2*x[19])/7)*sin(x[8])*cos(x[8]) + x[12]*x[14]*sin(x[8])*(x[17] - g__1)*cos(x[7])/21 + (2*x[13]*x[18]*sin(x[4]))/7 + x[12]*x[15]*sin(x[6])*sin(x[7])*sin(x[8])*(x[17] - g__1)/21)*cos(x[4])^2)/2 + 3*(((4*x[13]*(cos(x[7])^2 - 2)*(x[17] - g__1)*cos(x[8])^2)/3 + sin(x[4])*((2*x[18]*cos(x[7])^2*sin(x[8]))/3 + x[12]*sin(x[7])*(x[17] - g__1)*cos(x[7]) - (4*x[18]*sin(x[8]))/3)*cos(x[8]) - (2*x[13]*(cos(x[7])^2 - 2)*(x[17] - g__1))/3)*cos(x[6])^2 + ((4*x[18]*cos(x[8])^2*sin(x[4])*sin(x[7]))/3 - (8*x[13]*sin(x[7])*sin(x[8])*(x[17] - g__1)*cos(x[8]))/3 + (x[12]*sin(x[8])*(x[17] - g__1)*cos(x[7]) - (2*x[18]*sin(x[7]))/3)*sin(x[4]))*sin(x[6])*cos(x[6]) + (4*x[13]*(x[17] - g__1)*cos(x[8])^2)/3 + (2*x[18]*cos(x[8])*sin(x[4])*sin(x[8]))/3 - (2*x[13]*(x[17] - g__1))/3)*x[12]^2*cos(x[4]) + 2*(x[17] - g__1)*(cos(x[8])*sin(x[8])*(cos(x[7])^2 - 2)*cos(x[6])^2 + 2*(cos(x[8])^2 - 1/2)*sin(x[7])*sin(x[6])*cos(x[6]) + cos(x[8])*sin(x[8]))*x[12]^3)*L*cos(x[5])^6 + (12*m__1*sin(x[5])*((-((x[12]^2*x[18] - x[20]/6)*(cos(x[7])^2 - 2)*cos(x[8])^2)/2 + (x[12]^2*x[18] - x[20]/6)*cos(x[7])^2 + sin(x[7])*((x[17] - g__1)*x[12]^2 + (x[17] - g__1)*x[13]^2 - x[19]/2)*x[12]*sin(x[8])*cos(x[7]) - x[12]^2*x[18]/2 + x[20]/12)*cos(x[6])^2 - (((x[17] - g__1)*x[12]^2 + (x[17] - g__1)*x[13]^2 - x[19]/2)*x[12]*cos(x[7]) - (x[12]^2*x[18] - x[20]/6)*sin(x[7])*sin(x[8]))*cos(x[8])*sin(x[6])*cos(x[6]) - cos(x[8])^2*(x[12]^2*x[18] - x[20]/6)/2)*L*cos(x[4])^5 - 6*m__1*sin(x[5])*((sin(x[4])*(cos(x[7])^2 - 2)*((x[17] - g__1)*x[12]^2 + (x[17] - g__1)*x[13]^2 - x[19]/2)*x[12]*cos(x[8])^2 + 3*x[13]*((2*x[18]*cos(x[7])^2*sin(x[8]))/3 + x[12]*sin(x[7])*(x[17] - g__1)*cos(x[7]) - (4*x[18]*sin(x[8]))/3)*x[12]*cos(x[8]) - 2*sin(x[4])*(((x[17] - g__1)*x[12]^2 + (x[17] - g__1)*x[13]^2 - x[19]/2)*x[12]*cos(x[7])^2 - (x[12]^2*x[18] - x[20]/6)*sin(x[7])*sin(x[8])*cos(x[7]) - (((x[17] - g__1)*x[12]^2 + (x[17] - g__1)*x[13]^2 - x[19]/2)*x[12])/2))*cos(x[6])^2 - 2*(-2*x[12]*x[13]*x[18]*cos(x[8])^2*sin(x[7]) + sin(x[4])*((x[12]^2*x[18] - x[20]/6)*cos(x[7]) + sin(x[7])*((x[17] - g__1)*x[12]^2 + (x[17] - g__1)*x[13]^2 - x[19]/2)*x[12]*sin(x[8]))*cos(x[8]) - 3*(x[12]*sin(x[8])*(x[17] - g__1)*cos(x[7]) - (2*x[18]*sin(x[7]))/3)*x[13]*x[12]/2)*sin(x[6])*cos(x[6]) + cos(x[8])*(sin(x[4])*((x[17] - g__1)*x[12]^2 + (x[17] - g__1)*x[13]^2 - x[19]/2)*cos(x[8]) + 2*x[13]*x[18]*sin(x[8]))*x[12])*L*cos(x[4])^4 + ((15*m__1*sin(x[5])*(cos(x[7])^2 - 2)*(x[12]^2*x[18] - (2*x[20])/15)*L*cos(x[8])^2 - 18*x[12]*((x[17] - g__1)*(L*x[12]*x[13]*sin(x[4])*sin(x[5])*m__1 - 2*(m__1 + m__p)*(x[17] - g__1)/9)*sin(x[8])*cos(x[7])^2 - (2*L*x[13]*x[18]*cos(x[7])*sin(x[4])*sin(x[5])*sin(x[7])*m__1)/3 - 2*(x[17] - g__1)*(L*x[12]*x[13]*sin(x[4])*sin(x[5])*m__1 - 2*(m__1 + m__p)*(x[17] - g__1)/9)*sin(x[8]))*cos(x[8]) - 33*m__1*sin(x[5])*(((7*x[12]^2*x[18])/11 - x[20]/33)*cos(x[7])^2 + ((x[17] - g__1)*x[12]^2 + ((4*x[17])/11 - (4*g__1)/11)*x[13]^2 - (2*x[19])/11)*sin(x[7])*x[12]*sin(x[8])*cos(x[7]) - (5*x[12]^2*x[18])/11 + (2*x[20])/33)*L)*cos(x[6])^2 + 33*(-12*(x[17] - g__1)*(L*x[12]*x[13]*sin(x[4])*sin(x[5])*m__1 - 2*(m__1 + m__p)*(x[17] - g__1)/9)*sin(x[7])*x[12]*cos(x[8])^2/11 + m__1*sin(x[5])*(((x[17] - g__1)*x[12]^2 + ((4*x[17])/11 - (4*g__1)/11)*x[13]^2 - (2*x[19])/11)*x[12]*cos(x[7]) - 10*(x[12]^2*x[18] - (2*x[20])/15)*sin(x[7])*sin(x[8])/11)*L*cos(x[8]) + (6*x[12]*((2*L*x[13]*x[18]*cos(x[7])*sin(x[4])*sin(x[5])*sin(x[8])*m__1)/3 + (x[17] - g__1)*(L*x[12]*x[13]*sin(x[4])*sin(x[5])*m__1 - 2*(m__1 + m__p)*(x[17] - g__1)/9)*sin(x[7])))/11)*sin(x[6])*cos(x[6]) + 15*m__1*sin(x[5])*(x[12]^2*x[18] - (2*x[20])/15)*L*cos(x[8])^2 - 18*(x[17] - g__1)*(L*x[12]*x[13]*sin(x[4])*sin(x[5])*m__1 - 2*(m__1 + m__p)*(x[17] - g__1)/9)*x[12]*sin(x[8])*cos(x[8]) - 3*(x[12]^2*x[18] - x[20]/3)*m__1*sin(x[5])*L)*cos(x[4])^3 + 15*x[12]*((m__1*sin(x[4])*sin(x[5])*(cos(x[7])^2 - 2)*L*((x[17] - g__1)*x[12]^2 + ((4*x[17])/5 - (4*g__1)/5)*x[13]^2 - (2*x[19])/5)*cos(x[8])^2 + ((4*L*x[13]*x[18]*cos(x[7])^2*sin(x[5])*sin(x[8])*m__1)/5 + 2*(x[17] - g__1)*sin(x[7])*(L*x[12]*x[13]*sin(x[5])*m__1 - (2*sin(x[4])*(m__1 + m__p)*(x[17] - g__1))/15)*cos(x[7]) - (8*L*x[13]*x[18]*sin(x[5])*sin(x[8])*m__1)/5)*cos(x[8]) - (9*m__1*sin(x[4])*(((x[17] - g__1)*x[12]^2 + ((2*x[17])/9 - (2*g__1)/9)*x[13]^2 - x[19]/9)*cos(x[7])^2 - (5*x[12]*x[18]*cos(x[7])*sin(x[7])*sin(x[8]))/9 + (-(5*x[17])/9 + (5*g__1)/9)*x[12]^2 + (-(4*x[17])/9 + (4*g__1)/9)*x[13]^2 + (2*x[19])/9)*sin(x[5])*L)/5)*cos(x[6])^2 + ((8*L*x[13]*x[18]*cos(x[8])^2*sin(x[5])*sin(x[6])*sin(x[7])*m__1)/5 - 2*(x[12]*x[18]*cos(x[7])/2 + sin(x[7])*((x[17] - g__1)*x[12]^2 + ((4*x[17])/5 - (4*g__1)/5)*x[13]^2 - (2*x[19])/5)*sin(x[8]))*m__1*sin(x[4])*sin(x[5])*L*sin(x[6])*cos(x[8]) + 2*(x[17] - g__1)*(L*x[12]*x[13]*sin(x[5])*m__1 - (2*sin(x[4])*(m__1 + m__p)*(x[17] - g__1))/15)*sin(x[8])*sin(x[6])*cos(x[7]) - m__1*(x[12]*x[15]*sin(x[8])*(x[17] - g__1)*sin(x[4]) + 12*x[13]*x[18]*sin(x[6])*sin(x[7]))*sin(x[5])*L/15)*cos(x[6]) + m__1*sin(x[5])*(sin(x[4])*((x[17] - g__1)*x[12]^2 + ((4*x[17])/5 - (4*g__1)/5)*x[13]^2 - (2*x[19])/5)*cos(x[8])^2 + (x[12]*x[14]*sin(x[4])*(x[17] - g__1)*cos(x[7])/15 + x[12]*x[15]*sin(x[6])*sin(x[7])*(x[17] - g__1)*sin(x[4])/15 + (4*x[13]*x[18]*sin(x[8]))/5)*cos(x[8]) - sin(x[4])*((x[17] - g__1)*x[12]^2 + (2*x[17] - 2*g__1)*x[13]^2 - x[19])/5)*L)*cos(x[4])^2 + 18*x[12]*((-(2*L*x[12]*x[18]*sin(x[5])*m__1*(cos(x[7])^2 - 2)*cos(x[8])^2)/3 + 4*(x[17] - g__1)*(cos(x[7])^2 - 2)*sin(x[8])*(L*x[12]*x[13]*sin(x[4])*sin(x[5])*m__1 - ((m__1 + m__p)*(x[17] - g__1))/6)*cos(x[8])/3 + m__1*sin(x[5])*x[12]*L*(x[18]*cos(x[7])^2/3 + x[12]*sin(x[7])*sin(x[8])*(x[17] - g__1)*cos(x[7]) - (2*x[18])/3))*cos(x[6])^2 - (-8*(x[17] - g__1)*sin(x[7])*(L*x[12]*x[13]*sin(x[4])*sin(x[5])*m__1 - ((m__1 + m__p)*(x[17] - g__1))/6)*cos(x[8])^2/3 + m__1*sin(x[5])*(x[12]*cos(x[7])*(x[17] - g__1) - (4*x[18]*sin(x[7])*sin(x[8]))/3)*x[12]*L*cos(x[8]) + 4*(x[17] - g__1)*sin(x[7])*(L*x[12]*x[13]*sin(x[4])*sin(x[5])*m__1 - ((m__1 + m__p)*(x[17] - g__1))/6)/3)*sin(x[6])*cos(x[6]) - (2*L*x[12]*x[18]*cos(x[8])^2*sin(x[5])*m__1)/3 + 4*(x[17] - g__1)*sin(x[8])*(L*x[12]*x[13]*sin(x[4])*sin(x[5])*m__1 - ((m__1 + m__p)*(x[17] - g__1))/6)*cos(x[8])/3 + L*x[12]*x[18]*sin(x[5])*m__1/3)*cos(x[4]) - 12*(x[17] - g__1)*m__1*sin(x[4])*sin(x[5])*x[12]^3*L*((cos(x[8])^2 - 1/2)*(cos(x[7])^2 - 2)*cos(x[6])^2 - 2*cos(x[6])*sin(x[7])*cos(x[8])*sin(x[6])*sin(x[8]) + cos(x[8])^2 - 1/2))*cos(x[5])^5 + (-18*m__1*x[13]*L*(((cos(x[7])^2 - 2)*((x[17] - g__1)*x[12]^2 + (x[17]/3 - g__1/3)*x[13]^2 - x[19]/6)*cos(x[8])^2 + ((-2*x[17] + 2*g__1)*x[12]^2 + (-(2*x[17])/3 + (2*g__1)/3)*x[13]^2 + x[19]/3)*cos(x[7])^2 + (4*x[12]*x[18]*cos(x[7])*sin(x[7])*sin(x[8]))/3 + (x[17] - g__1)*x[12]^2 + (x[17]/3 - g__1/3)*x[13]^2 - x[19]/6)*cos(x[6])^2 - 2*((2*x[12]*x[18]*cos(x[7]))/3 + sin(x[7])*sin(x[8])*((x[17] - g__1)*x[12]^2 + (x[17]/3 - g__1/3)*x[13]^2 - x[19]/6))*cos(x[8])*sin(x[6])*cos(x[6]) + cos(x[8])^2*((x[17] - g__1)*x[12]^2 + (x[17]/3 - g__1/3)*x[13]^2 - x[19]/6))*cos(x[4])^5 + ((12*L*sin(x[4])*m__1*x[12]*x[13]*x[18]*(cos(x[7])^2 - 2)*cos(x[8])^2 - 12*m__1*L*(((x[17] - g__1)*x[12]^2 + ((9*x[17])/2 - (9*g__1)/2)*x[13]^2 - x[19]/2)*x[12]*sin(x[8])*cos(x[7])^2 - sin(x[7])*(x[12]^2*x[18] + 5/4*x[13]^2*x[18] - 1/6*x[20])*cos(x[7]) - 2*((x[17] - g__1)*x[12]^2 + ((9*x[17])/2 - (9*g__1)/2)*x[13]^2 - x[19]/2)*x[12]*sin(x[8]))*cos(x[8]) - 24*L*x[12]*x[13]*x[18]*cos(x[7])^2*sin(x[4])*m__1 - 36*sin(x[7])*(-x[12]*(x[17] - g__1)^2*(m__1 + m__p)*sin(x[5])/9 + m__1*sin(x[4])*x[13]*L*((x[17] - g__1)*x[12]^2 + (x[17]/3 - g__1/3)*x[13]^2 - x[19]/6))*sin(x[8])*cos(x[7]) + 12*L*sin(x[4])*m__1*x[12]*x[13]*x[18])*cos(x[6])^2 + (-24*m__1*((x[17] - g__1)*x[12]^2 + ((9*x[17])/2 - (9*g__1)/2)*x[13]^2 - x[19]/2)*sin(x[7])*x[12]*L*sin(x[6])*cos(x[8])^2 + (36*(-x[12]*(x[17] - g__1)^2*(m__1 + m__p)*sin(x[5])/9 + m__1*sin(x[4])*x[13]*L*((x[17] - g__1)*x[12]^2 + (x[17]/3 - g__1/3)*x[13]^2 - x[19]/6))*sin(x[6])*cos(x[7]) - 24*m__1*(x[12]*x[18]*sin(x[4])*sin(x[6])*sin(x[7])*sin(x[8]) - x[13]*x[15]*(x[17] - g__1)/24)*x[13]*L)*cos(x[8]) + 12*m__1*(sin(x[8])*(x[12]^2*x[18] + 5/4*x[13]^2*x[18] - 1/6*x[20])*cos(x[7]) + ((x[17] - g__1)*x[12]^2 + ((9*x[17])/2 - (9*g__1)/2)*x[13]^2 - x[19]/2)*sin(x[7])*x[12])*L*sin(x[6]))*cos(x[6]) - 12*m__1*(-x[12]*x[13]*x[18]*cos(x[8])^2*sin(x[4]) + ((x[17] - g__1)*x[12]^2 + ((9*x[17])/2 - (9*g__1)/2)*x[13]^2 - x[19]/2)*x[12]*sin(x[8])*cos(x[8]) - x[13]^2*sin(x[8])*(x[17] - g__1)*(sin(x[6])*sin(x[7])*x[15] + x[14]*cos(x[7]))/12)*L)*cos(x[4])^4 + ((63*(cos(x[7])^2 - 2)*(-(2*x[12]*sin(x[4])*(x[17] - g__1)^2*(m__1 + m__p)*sin(x[5]))/63 + m__1*x[13]*L*((x[17] - g__1)*x[12]^2 + ((2*x[17])/7 - (2*g__1)/7)*x[13]^2 - (2*x[19])/21))*cos(x[8])^2 + 12*m__1*sin(x[4])*(sin(x[8])*(x[12]^2*x[18] + 5/4*x[13]^2*x[18] - 1/6*x[20])*cos(x[7])^2 + ((x[17] - g__1)*x[12]^2 + ((9*x[17])/2 - (9*g__1)/2)*x[13]^2 - x[19]/2)*sin(x[7])*x[12]*cos(x[7]) - 2*sin(x[8])*(x[12]^2*x[18] + 5/4*x[13]^2*x[18] - 1/6*x[20]))*L*cos(x[8]) + (4*x[12]*sin(x[4])*(x[17] - g__1)^2*(m__1 + m__p)*sin(x[5]) - 63*m__1*((x[17] - g__1)*x[12]^2 - x[19]/21)*x[13]*L)*cos(x[7])^2 + 24*L*x[12]*x[13]*x[18]*cos(x[7])*sin(x[7])*sin(x[8])*m__1 - 2*x[12]*sin(x[4])*(x[17] - g__1)^2*(m__1 + m__p)*sin(x[5]) + 63*m__1*x[13]*L*((x[17] - g__1)*x[12]^2 + ((2*x[17])/7 - (2*g__1)/7)*x[13]^2 - (2*x[19])/21))*cos(x[6])^2 + 12*(2*m__1*sin(x[4])*sin(x[7])*L*(x[12]^2*x[18] + 5/4*x[13]^2*x[18] - 1/6*x[20])*cos(x[8])^2 + (-2*L*x[12]*x[13]*x[18]*cos(x[7])*m__1 - (21*sin(x[7])*(-(2*x[12]*sin(x[4])*(x[17] - g__1)^2*(m__1 + m__p)*sin(x[5]))/63 + m__1*x[13]*L*((x[17] - g__1)*x[12]^2 + ((2*x[17])/7 - (2*g__1)/7)*x[13]^2 - (2*x[19])/21))*sin(x[8]))/2)*cos(x[8]) + m__1*sin(x[4])*(((x[17] - g__1)*x[12]^2 + ((9*x[17])/2 - (9*g__1)/2)*x[13]^2 - x[19]/2)*x[12]*sin(x[8])*cos(x[7]) - sin(x[7])*(x[12]^2*x[18] + 5/4*x[13]^2*x[18] - 1/6*x[20]))*L)*sin(x[6])*cos(x[6]) + (-2*x[12]*sin(x[4])*(x[17] - g__1)^2*(m__1 + m__p)*sin(x[5]) + 63*m__1*x[13]*L*((x[17] - g__1)*x[12]^2 + ((2*x[17])/7 - (2*g__1)/7)*x[13]^2 - (2*x[19])/21))*cos(x[8])^2 + 12*m__1*sin(x[4])*L*(x[12]^2*x[18] + 5/4*x[13]^2*x[18] - 1/6*x[20])*sin(x[8])*cos(x[8]) - 27*m__1*x[13]*(-x[13]*x[15]*sin(x[4])*sin(x[6])*(x[17] - g__1)*cos(x[7])/27 + x[13]*x[14]*sin(x[7])*(x[17] - g__1)*sin(x[4])/27 + (x[17] - g__1)*x[12]^2 + ((4*x[17])/9 - (4*g__1)/9)*x[13]^2 - x[19]/9)*L)*cos(x[4])^3 + ((-30*L*sin(x[4])*m__1*x[12]*x[13]*x[18]*(cos(x[7])^2 - 2)*cos(x[8])^2 + 24*m__1*(((x[17] - g__1)*x[12]^2 + ((17*x[17])/8 - (17*g__1)/8)*x[13]^2 - x[19]/4)*x[12]*sin(x[8])*cos(x[7])^2 - (5*sin(x[7])*x[18]*(x[12]^2 - x[13]^2/5)*cos(x[7]))/8 - 2*((x[17] - g__1)*x[12]^2 + ((17*x[17])/8 - (17*g__1)/8)*x[13]^2 - x[19]/4)*x[12]*sin(x[8]))*L*cos(x[8]) + 12*L*x[12]*x[13]*x[18]*cos(x[7])^2*sin(x[4])*m__1 + 45*(x[17] - g__1)*sin(x[7])*(-(4*x[12]*(m__1 + m__p)*(x[17] - g__1)*sin(x[5]))/45 + L*x[13]*sin(x[4])*m__1*(x[12]^2 - (2*x[13]^2)/15))*sin(x[8])*cos(x[7]) - 30*L*sin(x[4])*m__1*x[12]*x[13]*x[18])*cos(x[6])^2 + (48*m__1*sin(x[7])*((x[17] - g__1)*x[12]^2 + ((17*x[17])/8 - (17*g__1)/8)*x[13]^2 - x[19]/4)*x[12]*L*sin(x[6])*cos(x[8])^2 + (-45*(x[17] - g__1)*(-(4*x[12]*(m__1 + m__p)*(x[17] - g__1)*sin(x[5]))/45 + L*x[13]*sin(x[4])*m__1*(x[12]^2 - (2*x[13]^2)/15))*sin(x[6])*cos(x[7]) + m__1*(60*x[12]*x[13]*x[18]*sin(x[4])*sin(x[6])*sin(x[7])*sin(x[8]) + x[15]*(x[12] - x[13])*(x[12] + x[13])*(x[17] - g__1))*L)*cos(x[8]) - 24*m__1*((5*x[18]*sin(x[8])*(x[12]^2 - x[13]^2/5)*cos(x[7]))/8 + sin(x[7])*((x[17] - g__1)*x[12]^2 + ((17*x[17])/8 - (17*g__1)/8)*x[13]^2 - x[19]/4)*x[12])*L*sin(x[6]))*cos(x[6]) + 24*m__1*(-(5*x[12]*x[13]*x[18]*cos(x[8])^2*sin(x[4]))/4 + ((x[17] - g__1)*x[12]^2 + ((17*x[17])/8 - (17*g__1)/8)*x[13]^2 - x[19]/4)*x[12]*sin(x[8])*cos(x[8]) + x[14]*sin(x[8])*(x[12] - x[13])*(x[12] + x[13])*(x[17] - g__1)*cos(x[7])/24 + (3*x[12]*x[13]*x[18]*sin(x[4]))/4 + x[15]*sin(x[6])*sin(x[7])*sin(x[8])*(x[12] - x[13])*(x[12] + x[13])*(x[17] - g__1)/24)*L)*cos(x[4])^2 - 18*x[12]*((8*(x[17] - g__1)*(cos(x[7])^2 - 2)*(-sin(x[4])*(m__1 + m__p)*(x[17] - g__1)*sin(x[5])/12 + L*x[12]*x[13]*m__1)*cos(x[8])^2/3 + m__1*sin(x[4])*((2*x[12]*x[18]*cos(x[7])^2*sin(x[8]))/3 + (x[17] - g__1)*(x[12]^2 - x[13]^2/3)*sin(x[7])*cos(x[7]) - (4*x[12]*x[18]*sin(x[8]))/3)*L*cos(x[8]) - (x[17] - g__1)*((-sin(x[4])*(m__1 + m__p)*(x[17] - g__1)*sin(x[5])/9 + L*x[12]*x[13]*m__1)*cos(x[7])^2 + (2*sin(x[4])*(m__1 + m__p)*(x[17] - g__1)*sin(x[5]))/9 - (8*L*x[12]*x[13]*m__1)/3))*cos(x[6])^2 + ((4*L*x[12]*x[18]*cos(x[8])^2*sin(x[4])*sin(x[7])*m__1)/3 - 16*(x[17] - g__1)*sin(x[7])*sin(x[8])*(-sin(x[4])*(m__1 + m__p)*(x[17] - g__1)*sin(x[5])/12 + L*x[12]*x[13]*m__1)*cos(x[8])/3 + m__1*sin(x[4])*((x[17] - g__1)*(x[12]^2 - x[13]^2/3)*sin(x[8])*cos(x[7]) - (2*x[12]*x[18]*sin(x[7]))/3)*L)*sin(x[6])*cos(x[6]) + 8*(x[17] - g__1)*(-sin(x[4])*(m__1 + m__p)*(x[17] - g__1)*sin(x[5])/12 + L*x[12]*x[13]*m__1)*cos(x[8])^2/3 + (2*L*x[12]*x[18]*cos(x[8])*sin(x[4])*sin(x[8])*m__1)/3 - 5*(x[17] - g__1)*(-sin(x[4])*(m__1 + m__p)*(x[17] - g__1)*sin(x[5])/15 + L*x[12]*x[13]*m__1)/3)*cos(x[4]) - 12*(x[17] - g__1)*m__1*(cos(x[8])*sin(x[8])*(cos(x[7])^2 - 2)*cos(x[6])^2 + 2*(cos(x[8])^2 - 1/2)*sin(x[7])*sin(x[6])*cos(x[6]) + cos(x[8])*sin(x[8]))*x[12]^3*L)*cos(x[5])^4 + (-36*m__1*sin(x[5])*x[13]^2*((-x[18]*(cos(x[7])^2 - 2)*cos(x[8])^2/6 + x[18]*cos(x[7])^2/3 + x[12]*sin(x[7])*sin(x[8])*(x[17] - g__1)*cos(x[7]) - x[18]/6)*cos(x[6])^2 - cos(x[8])*(x[12]*cos(x[7])*(x[17] - g__1) - x[18]*sin(x[7])*sin(x[8])/3)*sin(x[6])*cos(x[6]) - x[18]*cos(x[8])^2/6)*L*cos(x[4])^5 + 36*((((x[17] - g__1)*(cos(x[7])^2 - 2)*(L*x[12]*x[13]*sin(x[4])*sin(x[5])*m__1 - ((m__1 + m__p)*(x[17] - g__1))/9)*cos(x[8])^2)/2 + m__1*sin(x[5])*((2*x[12]*x[18]*cos(x[7])^2*sin(x[8]))/3 + sin(x[7])*((x[17] - g__1)*x[12]^2 + (x[17]/2 - g__1/2)*x[13]^2 - x[19]/6)*cos(x[7]) - (4*x[12]*x[18]*sin(x[8]))/3)*L*cos(x[8]) - (x[17] - g__1)*(L*x[12]*x[13]*sin(x[4])*sin(x[5])*m__1 - ((m__1 + m__p)*(x[17] - g__1))/9)*cos(x[7])^2 + L*x[13]*x[18]*cos(x[7])*sin(x[4])*sin(x[5])*sin(x[7])*sin(x[8])*m__1/3 + ((x[17] - g__1)*(L*x[12]*x[13]*sin(x[4])*sin(x[5])*m__1 - ((m__1 + m__p)*(x[17] - g__1))/9))/2)*cos(x[6])^2 + ((4*L*x[12]*x[18]*cos(x[8])^2*sin(x[5])*sin(x[7])*m__1)/3 + (-L*x[13]*x[18]*cos(x[7])*sin(x[4])*sin(x[5])*m__1/3 - (x[17] - g__1)*sin(x[7])*(L*x[12]*x[13]*sin(x[4])*sin(x[5])*m__1 - ((m__1 + m__p)*(x[17] - g__1))/9)*sin(x[8]))*cos(x[8]) + m__1*sin(x[5])*L*(sin(x[8])*((x[17] - g__1)*x[12]^2 + (x[17]/2 - g__1/2)*x[13]^2 - x[19]/6)*cos(x[7]) - (2*x[12]*x[18]*sin(x[7]))/3))*sin(x[6])*cos(x[6]) + cos(x[8])*((x[17] - g__1)*(L*x[12]*x[13]*sin(x[4])*sin(x[5])*m__1 - ((m__1 + m__p)*(x[17] - g__1))/9)*cos(x[8]) + (4*L*x[12]*x[18]*sin(x[5])*sin(x[8])*m__1)/3)/2)*x[13]*cos(x[4])^4 + ((-6*m__1*sin(x[5])*(cos(x[7])^2 - 2)*L*(x[12]^2*x[18] + 5/2*x[13]^2*x[18] - 1/6*x[20])*cos(x[8])^2 + (36*(m__1*sin(x[4])*x[13]*L*((x[17] - g__1)*x[12]^2 + (x[17]/2 - g__1/2)*x[13]^2 - x[19]/6)*sin(x[5]) - (11*x[12]*(x[17] - g__1)^2*(m__1 + m__p))/36)*sin(x[8])*cos(x[7])^2 - 24*sin(x[7])*x[18]*(L*x[12]*x[13]*sin(x[4])*sin(x[5])*m__1 - ((m__1 + m__p)*(x[17] - g__1))/6)*cos(x[7]) - 72*(m__1*sin(x[4])*x[13]*L*((x[17] - g__1)*x[12]^2 + (x[17]/2 - g__1/2)*x[13]^2 - x[19]/6)*sin(x[5]) - (11*x[12]*(x[17] - g__1)^2*(m__1 + m__p))/36)*sin(x[8]))*cos(x[8]) + 3*L*x[13]^2*x[18]*cos(x[7])^2*sin(x[5])*m__1 + 27*(x[17] - g__1)*x[13]*sin(x[7])*(L*x[12]*x[13]*sin(x[5])*m__1 - (4*sin(x[4])*(m__1 + m__p)*(x[17] - g__1))/27)*sin(x[8])*cos(x[7]) - 6*m__1*sin(x[5])*L*(x[12]^2*x[18] + 5/2*x[13]^2*x[18] - 1/6*x[20]))*cos(x[6])^2 + (72*(m__1*sin(x[4])*x[13]*L*((x[17] - g__1)*x[12]^2 + (x[17]/2 - g__1/2)*x[13]^2 - x[19]/6)*sin(x[5]) - (11*x[12]*(x[17] - g__1)^2*(m__1 + m__p))/36)*sin(x[7])*sin(x[6])*cos(x[8])^2 + (-27*(x[17] - g__1)*x[13]*(L*x[12]*x[13]*sin(x[5])*m__1 - (4*sin(x[4])*(m__1 + m__p)*(x[17] - g__1))/27)*sin(x[6])*cos(x[7]) + 12*m__1*sin(x[7])*L*(x[12]^2*x[18] + 5/2*x[13]^2*x[18] - 1/6*x[20])*sin(x[8])*sin(x[6])*sin(x[5]) + x[15]*(x[17] - g__1)^2*(m__1 + m__p))*cos(x[8]) - 36*((2*x[18]*sin(x[8])*(L*x[12]*x[13]*sin(x[4])*sin(x[5])*m__1 - ((m__1 + m__p)*(x[17] - g__1))/6)*cos(x[7]))/3 + (m__1*sin(x[4])*x[13]*L*((x[17] - g__1)*x[12]^2 + (x[17]/2 - g__1/2)*x[13]^2 - x[19]/6)*sin(x[5]) - (11*x[12]*(x[17] - g__1)^2*(m__1 + m__p))/36)*sin(x[7]))*sin(x[6]))*cos(x[6]) - 6*m__1*sin(x[5])*L*(x[12]^2*x[18] + 5/2*x[13]^2*x[18] - 1/6*x[20])*cos(x[8])^2 + 36*(m__1*sin(x[4])*x[13]*L*((x[17] - g__1)*x[12]^2 + (x[17]/2 - g__1/2)*x[13]^2 - x[19]/6)*sin(x[5]) - (11*x[12]*(x[17] - g__1)^2*(m__1 + m__p))/36)*sin(x[8])*cos(x[8]) + x[14]*sin(x[8])*(x[17] - g__1)^2*(m__1 + m__p)*cos(x[7]) + 6*m__1*(x[12]^2*x[18] + 3/2*x[13]^2*x[18] - 1/6*x[20])*L*sin(x[5]) + x[15]*sin(x[6])*sin(x[7])*sin(x[8])*(x[17] - g__1)^2*(m__1 + m__p))*cos(x[4])^3 + ((-6*(cos(x[7])^2 - 2)*(m__1*sin(x[4])*x[12]*((x[17] - g__1)*x[12]^2 + ((15*x[17])/2 - (15*g__1)/2)*x[13]^2 - x[19]/2)*L*sin(x[5]) - (11*x[13]*(x[17] - g__1)^2*(m__1 + m__p))/6)*cos(x[8])^2 + (-24*(L*x[12]*x[13]*sin(x[5])*m__1 - sin(x[4])*(m__1 + m__p)*(x[17] - g__1)/6)*x[18]*sin(x[8])*cos(x[7])^2 - 42*(x[17] - g__1)*(L*x[13]*m__1*(x[12]^2 - x[13]^2/7)*sin(x[5]) - (11*x[12]*sin(x[4])*(m__1 + m__p)*(x[17] - g__1))/42)*sin(x[7])*cos(x[7]) + 48*(L*x[12]*x[13]*sin(x[5])*m__1 - sin(x[4])*(m__1 + m__p)*(x[17] - g__1)/6)*x[18]*sin(x[8]))*cos(x[8]) + 9*(x[17] - g__1)*(L*x[12]*x[13]*sin(x[4])*sin(x[5])*m__1 + 5*(m__1 + m__p)*(x[17] - g__1)/9)*x[13]*cos(x[7])^2 + 3*L*x[13]^2*x[18]*cos(x[7])*sin(x[4])*sin(x[5])*sin(x[7])*sin(x[8])*m__1 - 6*m__1*sin(x[4])*x[12]*((x[17] - g__1)*x[12]^2 + ((15*x[17])/2 - (15*g__1)/2)*x[13]^2 - x[19]/2)*L*sin(x[5]) + 11*x[13]*(x[17] - g__1)^2*(m__1 + m__p))*cos(x[6])^2 + (-48*(L*x[12]*x[13]*sin(x[5])*m__1 - sin(x[4])*(m__1 + m__p)*(x[17] - g__1)/6)*sin(x[7])*x[18]*sin(x[6])*cos(x[8])^2 + 12*(-L*x[13]^2*x[18]*cos(x[7])*sin(x[4])*sin(x[5])*m__1/4 + sin(x[7])*(m__1*sin(x[4])*x[12]*((x[17] - g__1)*x[12]^2 + ((15*x[17])/2 - (15*g__1)/2)*x[13]^2 - x[19]/2)*L*sin(x[5]) - (11*x[13]*(x[17] - g__1)^2*(m__1 + m__p))/6)*sin(x[8]))*sin(x[6])*cos(x[8]) - 42*(x[17] - g__1)*(L*x[13]*m__1*(x[12]^2 - x[13]^2/7)*sin(x[5]) - (11*x[12]*sin(x[4])*(m__1 + m__p)*(x[17] - g__1))/42)*sin(x[8])*sin(x[6])*cos(x[7]) + 24*m__1*(-x[13]*x[15]*sin(x[8])*(x[17] - g__1)*sin(x[4])/24 + x[12]*x[18]*sin(x[6])*sin(x[7]))*x[13]*L*sin(x[5]) - 4*x[18]*sin(x[4])*sin(x[6])*sin(x[7])*(m__1 + m__p)*(x[17] - g__1))*cos(x[6]) + (-6*m__1*sin(x[4])*x[12]*((x[17] - g__1)*x[12]^2 + ((15*x[17])/2 - (15*g__1)/2)*x[13]^2 - x[19]/2)*L*sin(x[5]) + 11*x[13]*(x[17] - g__1)^2*(m__1 + m__p))*cos(x[8])^2 + (L*x[13]^2*x[14]*sin(x[4])*sin(x[5])*m__1*(x[17] - g__1)*cos(x[7]) - 24*m__1*(-x[13]*x[15]*sin(x[6])*sin(x[7])*(x[17] - g__1)*sin(x[4])/24 + x[12]*x[18]*sin(x[8]))*x[13]*L*sin(x[5]) + 4*x[18]*sin(x[4])*sin(x[8])*(m__1 + m__p)*(x[17] - g__1))*cos(x[8]) + x[15]*sin(x[4])*sin(x[6])*(x[17] - g__1)^2*(m__1 + m__p)*cos(x[7]) + 6*m__1*sin(x[4])*((x[17] - g__1)*x[12]^2 + ((9*x[17])/2 - (9*g__1)/2)*x[13]^2 - x[19]/2)*x[12]*L*sin(x[5]) - 9*(x[17] - g__1)^2*(x[14]*sin(x[4])*sin(x[7])/9 + x[13])*(m__1 + m__p))*cos(x[4])^2 + ((6*L*sin(x[5])*m__1*x[12]^2*x[18]*(cos(x[7])^2 - 2)*cos(x[8])^2 - 36*(x[17] - g__1)*((L*x[12]*x[13]*sin(x[4])*sin(x[5])*m__1 - 2*(m__1 + m__p)*(x[17] - g__1)/9)*x[12]*sin(x[8])*cos(x[7])^2 - x[18]*sin(x[7])*(m__1 + m__p)*cos(x[7])/9 - 2*(L*x[12]*x[13]*sin(x[4])*sin(x[5])*m__1 - 2*(m__1 + m__p)*(x[17] - g__1)/9)*x[12]*sin(x[8]))*cos(x[8]) + 6*(x[17] - g__1)*x[13]*sin(x[7])*(L*x[12]*x[13]*sin(x[5])*m__1 - (7*sin(x[4])*(m__1 + m__p)*(x[17] - g__1))/6)*sin(x[8])*cos(x[7]) + 6*L*sin(x[5])*m__1*x[12]^2*x[18])*cos(x[6])^2 + (-72*(x[17] - g__1)*(L*x[12]*x[13]*sin(x[4])*sin(x[5])*m__1 - 2*(m__1 + m__p)*(x[17] - g__1)/9)*sin(x[7])*x[12]*sin(x[6])*cos(x[8])^2 + (-6*(x[17] - g__1)*x[13]*(L*x[12]*x[13]*sin(x[5])*m__1 - (7*sin(x[4])*(m__1 + m__p)*(x[17] - g__1))/6)*sin(x[6])*cos(x[7]) - 12*L*x[12]^2*x[18]*sin(x[5])*sin(x[6])*sin(x[7])*sin(x[8])*m__1 - x[15]*(x[17] - g__1)^2*(m__1 + m__p))*cos(x[8]) + 36*(x[17] - g__1)*(x[18]*sin(x[8])*(m__1 + m__p)*cos(x[7])/9 + (L*x[12]*x[13]*sin(x[4])*sin(x[5])*m__1 - 2*(m__1 + m__p)*(x[17] - g__1)/9)*sin(x[7])*x[12])*sin(x[6]))*cos(x[6]) + 6*L*sin(x[5])*cos(x[8])^2*m__1*x[12]^2*x[18] - 36*(x[17] - g__1)*(L*x[12]*x[13]*sin(x[4])*sin(x[5])*m__1 - 2*(m__1 + m__p)*(x[17] - g__1)/9)*x[12]*sin(x[8])*cos(x[8]) - x[14]*sin(x[8])*(x[17] - g__1)^2*(m__1 + m__p)*cos(x[7]) - 6*L*sin(x[5])*m__1*x[12]^2*x[18] - x[15]*sin(x[6])*sin(x[7])*sin(x[8])*(x[17] - g__1)^2*(m__1 + m__p))*cos(x[4]) + 6*(x[17] - g__1)*sin(x[4])*x[12]*((L*x[12]^2*sin(x[5])*m__1*(cos(x[7])^2 - 2)*cos(x[8])^2 + (7*cos(x[7])*sin(x[7])*(m__1 + m__p)*(x[17] - g__1)*cos(x[8]))/6 + L*x[12]^2*sin(x[5])*m__1)*cos(x[6])^2 - 2*(L*x[12]^2*cos(x[8])*sin(x[5])*sin(x[7])*m__1 - (7*cos(x[7])*(m__1 + m__p)*(x[17] - g__1))/12)*sin(x[8])*sin(x[6])*cos(x[6]) + L*x[12]^2*sin(x[5])*m__1*(cos(x[8]) - 1)*(cos(x[8]) + 1)))*cos(x[5])^3 + (6*(((cos(x[7])^2 - 2)*cos(x[8])^2 - 2*cos(x[7])^2 + 1)*cos(x[6])^2 - 2*cos(x[6])*sin(x[7])*cos(x[8])*sin(x[6])*sin(x[8]) + cos(x[8])^2)*(x[17] - g__1)*m__1*x[13]^3*L*cos(x[4])^5 + 36*m__1*x[13]^2*(((x[12]*sin(x[8])*(x[17] - g__1)*cos(x[7])^2 - x[18]*cos(x[7])*sin(x[7])/3 - 2*x[12]*sin(x[8])*(x[17] - g__1))*cos(x[8]) + x[13]*cos(x[7])*sin(x[4])*sin(x[7])*sin(x[8])*(x[17] - g__1)/3)*cos(x[6])^2 + 2*(x[12]*sin(x[7])*(x[17] - g__1)*cos(x[8])^2 - x[13]*sin(x[4])*cos(x[7])*(x[17] - g__1)*cos(x[8])/6 - x[18]*cos(x[7])*sin(x[8])/6 - x[12]*sin(x[7])*(x[17] - g__1)/2)*sin(x[6])*cos(x[6]) + x[12]*cos(x[8])*sin(x[8])*(x[17] - g__1))*L*cos(x[4])^4 - 18*x[13]*((m__1*((x[17] - g__1)*x[12]^2 + ((7*x[17])/6 - (7*g__1)/6)*x[13]^2 - x[19]/6)*(cos(x[7])^2 - 2)*L*cos(x[8])^2 + ((2*L*x[13]*x[18]*cos(x[7])^2*sin(x[4])*sin(x[8])*m__1)/3 + 2*(x[17] - g__1)*(-11*(m__1 + m__p)*(x[17] - g__1)*sin(x[5])/36 + L*x[12]*x[13]*sin(x[4])*m__1)*sin(x[7])*cos(x[7]) - (4*L*x[13]*x[18]*sin(x[4])*sin(x[8])*m__1)/3)*cos(x[8]) + m__1*(((x[17] - g__1)*x[13]^2*cos(x[7])^2)/6 + (x[17] - g__1)*x[12]^2 + ((7*x[17])/6 - (7*g__1)/6)*x[13]^2 - x[19]/6)*L)*cos(x[6])^2 - 2*(-(2*L*x[13]*x[18]*cos(x[8])^2*sin(x[4])*sin(x[7])*m__1)/3 + m__1*((x[17] - g__1)*x[12]^2 + ((7*x[17])/6 - (7*g__1)/6)*x[13]^2 - x[19]/6)*sin(x[7])*L*sin(x[8])*cos(x[8]) - (x[17] - g__1)*(-11*(m__1 + m__p)*(x[17] - g__1)*sin(x[5])/36 + L*x[12]*x[13]*sin(x[4])*m__1)*sin(x[8])*cos(x[7]) + L*x[13]*x[18]*sin(x[4])*sin(x[7])*m__1/3)*sin(x[6])*cos(x[6]) + (((x[17] - g__1)*x[12]^2 + ((7*x[17])/6 - (7*g__1)/6)*x[13]^2 - x[19]/6)*cos(x[8])^2 + (2*x[13]*x[18]*cos(x[8])*sin(x[4])*sin(x[8]))/3 + (g__1 - x[17])*x[12]^2 + (-(5*x[17])/6 + (5*g__1)/6)*x[13]^2 + x[19]/6)*m__1*L)*cos(x[4])^3 + ((12*(-((m__1 + m__p)*(x[17] - g__1)*sin(x[5]))/3 + L*x[12]*x[13]*sin(x[4])*m__1)*(cos(x[7])^2 - 2)*x[18]*cos(x[8])^2 - 36*x[13]*((x[17] - g__1)*sin(x[8])*(-(11*sin(x[4])*(m__1 + m__p)*(x[17] - g__1)*sin(x[5]))/36 + L*x[12]*x[13]*m__1)*cos(x[7])^2 + L*x[13]*x[18]*cos(x[7])*sin(x[7])*m__1/12 - 2*(x[17] - g__1)*sin(x[8])*(-(11*sin(x[4])*(m__1 + m__p)*(x[17] - g__1)*sin(x[5]))/36 + L*x[12]*x[13]*m__1))*cos(x[8]) - 4*x[18]*sin(x[5])*(m__1 + m__p)*(x[17] - g__1)*cos(x[7])^2 + 9*(x[17] - g__1)*(-(10*x[12]*(m__1 + m__p)*(x[17] - g__1)*sin(x[5]))/9 + L*x[13]^3*sin(x[4])*m__1)*sin(x[7])*sin(x[8])*cos(x[7]) + 12*(-((m__1 + m__p)*(x[17] - g__1)*sin(x[5]))/3 + L*x[12]*x[13]*sin(x[4])*m__1)*x[18])*cos(x[6])^2 + (-72*(x[17] - g__1)*x[13]*sin(x[7])*(-(11*sin(x[4])*(m__1 + m__p)*(x[17] - g__1)*sin(x[5]))/36 + L*x[12]*x[13]*m__1)*sin(x[6])*cos(x[8])^2 + (-9*(x[17] - g__1)*(-(10*x[12]*(m__1 + m__p)*(x[17] - g__1)*sin(x[5]))/9 + L*x[13]^3*sin(x[4])*m__1)*sin(x[6])*cos(x[7]) + 8*x[18]*sin(x[6])*sin(x[7])*sin(x[8])*(m__1 + m__p)*(x[17] - g__1)*sin(x[5]) - 24*m__1*(x[12]*x[18]*sin(x[4])*sin(x[6])*sin(x[7])*sin(x[8]) - x[13]*x[15]*(x[17] - g__1)/24)*x[13]*L)*cos(x[8]) + 36*(-L*x[13]*x[18]*cos(x[7])*sin(x[8])*m__1/12 + (x[17] - g__1)*sin(x[7])*(-(11*sin(x[4])*(m__1 + m__p)*(x[17] - g__1)*sin(x[5]))/36 + L*x[12]*x[13]*m__1))*x[13]*sin(x[6]))*cos(x[6]) + 12*(-((m__1 + m__p)*(x[17] - g__1)*sin(x[5]))/3 + L*x[12]*x[13]*sin(x[4])*m__1)*x[18]*cos(x[8])^2 - 36*(x[17] - g__1)*x[13]*sin(x[8])*(-(11*sin(x[4])*(m__1 + m__p)*(x[17] - g__1)*sin(x[5]))/36 + L*x[12]*x[13]*m__1)*cos(x[8]) + L*x[13]^2*x[14]*sin(x[8])*m__1*(x[17] - g__1)*cos(x[7]) + 4*x[18]*sin(x[5])*(m__1 + m__p)*(x[17] - g__1) - 12*m__1*x[13]*L*(x[12]*x[18]*sin(x[4]) - x[13]*x[15]*sin(x[6])*sin(x[7])*sin(x[8])*(x[17] - g__1)/12))*cos(x[4])^2 + 18*(x[17] - g__1)*(((cos(x[7])^2 - 2)*x[12]*(-sin(x[4])*(m__1 + m__p)*(x[17] - g__1)*sin(x[5])/3 + L*x[12]*x[13]*m__1)*cos(x[8])^2 - ((-7*(m__1 + m__p)*(x[17] - g__1)*sin(x[5])/6 + L*x[12]*x[13]*sin(x[4])*m__1)*x[13]*sin(x[7])*cos(x[7])*cos(x[8]))/3 - (5*x[12]*sin(x[4])*sin(x[5])*(m__1 + m__p)*(x[17] - g__1)*cos(x[7])^2)/9 + (2*x[18]*sin(x[4])*sin(x[5])*sin(x[7])*sin(x[8])*(m__1 + m__p)*cos(x[7]))/9 + x[12]*(-sin(x[4])*(m__1 + m__p)*(x[17] - g__1)*sin(x[5])/3 + L*x[12]*x[13]*m__1))*cos(x[6])^2 + (-2*(x[18]*sin(x[4])*sin(x[5])*(m__1 + m__p)*cos(x[7])/9 + sin(x[7])*x[12]*(-sin(x[4])*(m__1 + m__p)*(x[17] - g__1)*sin(x[5])/3 + L*x[12]*x[13]*m__1)*sin(x[8]))*sin(x[6])*cos(x[8]) - (((-7*(m__1 + m__p)*(x[17] - g__1)*sin(x[5])/6 + L*x[12]*x[13]*sin(x[4])*m__1)*x[13]*sin(x[6])*cos(x[7]) + x[15]*sin(x[4])*sin(x[5])*(m__1 + m__p)*(x[17] - g__1)/6)*sin(x[8]))/3)*cos(x[6]) + x[12]*(-sin(x[4])*(m__1 + m__p)*(x[17] - g__1)*sin(x[5])/3 + L*x[12]*x[13]*m__1)*cos(x[8])^2 + sin(x[4])*sin(x[5])*(m__1 + m__p)*(x[17] - g__1)*(sin(x[6])*sin(x[7])*x[15] + x[14]*cos(x[7]))*cos(x[8])/18 - x[12]*(-sin(x[4])*(m__1 + m__p)*(x[17] - g__1)*sin(x[5])/3 + L*x[12]*x[13]*m__1))*cos(x[4]) + 7*x[12]*cos(x[6])*cos(x[7])*sin(x[5])*(x[17] - g__1)^2*(m__1 + m__p)*(cos(x[6])*sin(x[7])*sin(x[8]) - sin(x[6])*cos(x[8])))*cos(x[5])^2 + (-12*L*x[13]^3*cos(x[6])*cos(x[7])*sin(x[5])*m__1*(cos(x[6])*sin(x[7])*cos(x[8]) + sin(x[6])*sin(x[8]))*(x[17] - g__1)*cos(x[4])^4 - 12*m__1*sin(x[5])*x[13]^2*(((-x[18]*cos(x[7])^2/2 + x[18])*cos(x[8])^2 + x[13]*sin(x[4])*sin(x[8])*(cos(x[7])^2 - 2)*(x[17] - g__1)*cos(x[8]) - x[18]/2)*cos(x[6])^2 + 2*(x[13]*sin(x[4])*(x[17] - g__1)*cos(x[8])^2 + x[18]*cos(x[8])*sin(x[8])/2 - x[13]*sin(x[4])*(x[17] - g__1)/2)*sin(x[7])*sin(x[6])*cos(x[6]) - x[18]*cos(x[8])^2/2 + x[13]*sin(x[4])*sin(x[8])*(x[17] - g__1)*cos(x[8]) + x[18]/2)*L*cos(x[4])^3 + 18*(x[17] - g__1)*x[13]*(((L*x[12]*x[13]*sin(x[4])*sin(x[5])*m__1 - ((m__1 + m__p)*(x[17] - g__1))/3)*(cos(x[7])^2 - 2)*cos(x[8])^2 - L*x[13]^2*cos(x[7])*cos(x[8])*sin(x[5])*sin(x[7])*m__1/3 - 5*(m__1 + m__p)*(x[17] - g__1)*cos(x[7])^2/9 + L*x[12]*x[13]*sin(x[4])*sin(x[5])*m__1 - ((m__1 + m__p)*(x[17] - g__1))/3)*cos(x[6])^2 - 2*sin(x[8])*((L*x[12]*x[13]*sin(x[4])*sin(x[5])*m__1 - ((m__1 + m__p)*(x[17] - g__1))/3)*sin(x[7])*cos(x[8]) + L*x[13]^2*cos(x[7])*sin(x[5])*m__1/6)*sin(x[6])*cos(x[6]) + (cos(x[8]) + 1)*(L*x[12]*x[13]*sin(x[4])*sin(x[5])*m__1 - ((m__1 + m__p)*(x[17] - g__1))/3)*(cos(x[8]) - 1))*cos(x[4])^2 + 10*(x[17] - g__1)*(sin(x[7])*cos(x[7])*(-(2*x[18]*cos(x[8]))/5 + x[13]*sin(x[4])*sin(x[8])*(x[17] - g__1))*cos(x[6])^2 + (-(x[17] - g__1)*(x[13]*cos(x[7])*sin(x[4])*sin(x[6]) - x[15]/10)*cos(x[8]) - (2*x[18]*cos(x[7])*sin(x[6])*sin(x[8]))/5)*cos(x[6]) + sin(x[8])*(x[17] - g__1)*(sin(x[6])*sin(x[7])*x[15] + x[14]*cos(x[7]))/10)*(m__1 + m__p)*cos(x[4]) - 7*x[12]*cos(x[6])*cos(x[7])*sin(x[4])*(x[17] - g__1)^2*(m__1 + m__p)*(cos(x[6])*sin(x[7])*cos(x[8]) + sin(x[6])*sin(x[8])))*cos(x[5]) + 6*(x[17] - g__1)*cos(x[4])*x[13]*(((1 + (cos(x[7])^2 - 2)*cos(x[8])^2)*cos(x[6])^2 - 2*cos(x[6])*sin(x[7])*cos(x[8])*sin(x[6])*sin(x[8]) + cos(x[8])^2 - 1)*m__1*x[13]^2*L*cos(x[4])^2 - (7*cos(x[6])*cos(x[7])*sin(x[5])*(m__1 + m__p)*(cos(x[6])*sin(x[7])*cos(x[8]) + sin(x[6])*sin(x[8]))*(x[17] - g__1))/6))/(cos(x[4])^4*m__1*(((((cos(x[7])^2 - 2)*cos(x[8])^2 - 2*cos(x[7])^2 + 1)*cos(x[6])^2 - 2*cos(x[6])*sin(x[7])*cos(x[8])*sin(x[6])*sin(x[8]) + cos(x[8])^2)*cos(x[4])^2 + 2*cos(x[6])*cos(x[7])*sin(x[4])*(cos(x[6])*sin(x[7])*sin(x[8]) - sin(x[6])*cos(x[8]))*cos(x[4]) - 2*(cos(x[8])^2 - 1/2)*(cos(x[7])^2 - 2)*cos(x[6])^2 + 4*cos(x[6])*sin(x[7])*cos(x[8])*sin(x[6])*sin(x[8]) - 2*cos(x[8])^2 + 1)*cos(x[5])^2 - 2*sin(x[5])*(cos(x[6])*cos(x[7])*(cos(x[6])*sin(x[7])*cos(x[8]) + sin(x[6])*sin(x[8]))*cos(x[4]) + sin(x[4])*(cos(x[8])*sin(x[8])*(cos(x[7])^2 - 2)*cos(x[6])^2 + 2*(cos(x[8])^2 - 1/2)*sin(x[7])*sin(x[6])*cos(x[6]) + cos(x[8])*sin(x[8])))*cos(x[5]) + (1 + (cos(x[7])^2 - 2)*cos(x[8])^2)*cos(x[6])^2 - 2*cos(x[6])*sin(x[7])*cos(x[8])*sin(x[6])*sin(x[8]) + cos(x[8])^2 - 1)*L*cos(x[5])^4)

This worksheet displays an ellipsoid internally tangent to the four sides of a tetrahedron.

The tetrahedron is a special case: it has a horizontal base with vertices A,B and C and its fourth vertex E is on the z axis.

However I have failed when trying to display an internally tangent ellipsoid in any other tetrahedron.

Will any tetrahedron support one or more internally tangent ellipsoids?

If so, are there conditions restricting the location of the mutual points of tangency?

Ellipsoid_in_a_tetrahedron.mw

Maple 2021.1/Windows 10.

When entering 2d expressions into the bottom line of a worksheet, i.e. at the bottom of the window, I can't see the underscores used to indicate bracketing.

A workaround is to use ^J to get another input prompt at the bottom of the window.

Is there some way to get a bigger margin at the bottom of the window?

Cheers,

Steve.

The square root of x+8-square root of x+9-square root of 2x+4

restart;
with(plots); with(LinearAlgebra);
_EnvHorizontalName := 'x';

_EnvVerticalName := 'y';

x1,y1,x2,y2,x3,y3:=0,-3,3,1,5,-2:   
A := [x1, y1]: B := [x2, y2]: C := [x3, y3]:

Barycentre := proc (A, B, t) description "Barycentre de 2 points A(1) et B(t) dans le rapport t";
return [(1-t)*A[1]+t*B[1], (1-t)*A[2]+t*B[2]] end proc;
ellip := proc (r1, r2) local a, b, c, d, e, f, D, E, F, eq1, eq2, eq3, eq4, eq5, eq6, x0, y0, EE, r3, sol, Ff, Tg;
global A, B, C;
r3 := -1/(r2*r1);
D := Barycentre(C, B, 1/(1-r1)); E := Barycentre(A, C, 1/(1-r2)); F := Barycentre(B, A, 1/(1-r3));
Ff := proc (x, y) options operator, arrow; a*x^2+2*b*x*y+c*y^2+2*d*x+2*e*y+f end proc;
Tg := proc (x0, y0, x, y) options operator, arrow; a*x*x0+b*(x*y0+y*x0)+c*y*y0+d*(x+x0)+e*(y+y0)+f end proc;
eq1 := Ff(D[1], D[2]);
eq2 := Ff(E[1], E[2]);
eq3 := Ff(F[1], F[2]);
eq4 := Tg(F[1], F[2], x1, y1);
eq5 := Tg(D[1], D[2], x2, y2);
eq6 := Tg(E[1], E[2], x3, y3);
sol := op(solve([eq1, eq2, eq3, eq4, eq5, eq6], [a, b, c, d, e]));
assign(sol);
EE := subs(f = 1, Ff(x, y) = 0) end proc;

ellip(-1, -7); tri := plot([A, B, C, A], color = blue):
 
po := plot([A, B, C], style = point, symbolsize = 15, symbol = solidcircle, color = red);
tp := textplot([[A[], "A"], [B[], "B"], [C[], "C"]], 'align' = {'above', 'left'});
x := 'x'; y := 'y';
ELL := seq(implicitplot(ellip(-7/11-(1/11)*j, -1/17-3*j*(1/17)), x = 0 .. 5, y = -3 .. 1, color = ColorTools:-Color([rand()/10^12, rand()/10^12, rand()/10^12])), j = 1 .. 17);
display([tri, ELL, po, tp], view = [-.5 .. 5.5, -4 .. 1.5], axes = none, scaling = constrained, size = [500, 500]);
Explore(implicitplot(ellip(r1, r2), x = 0 .. 5, y = -3 .. 1), parameters = [r1 = -2.18 .. -.7, r2 = -3 .. -.23]);
Can you tell me why this last instruction does't work ? Thank you.
 

I rewrite my code with Grid library using local vCPU of amazon 

discover no license of distributed HPC when setup command show need go to acresso.com

can Grid still be used and function with local 96 number of vCPU?

then when I test code, I can not pkill mserver in ps -aux in LInux 

can the performance really improved ? Because I suppose 3 to 5 minutes mserver will end and disappear from ps -aux but grid node of mserver still running

originally I can run 100 batches every day., but I have to monitor decrease of memory in order to determine whether can kill mserver for next batch 

I expect run 400 batches per day. But Can not kill mserver when using grid

In my code I had using time limit(30, ...) 

when using Grid seq of function , can lprint work normally to get results into text ?

i notice Grid up to 57, do I need to recalculate and revise code to fit 96 vCPU for grid number 96?

Hi MaplePrimes team,

I am aware that Maple is not designed for CAD and I am not here for you to help me build any advanced system like the example below.

Figure 1: Trimmed surface of fuselage to create airplane windows.

Here I my problem. Even using the adaptmesh option, creating serious trimmed surfaces requires large numbers of grids like for example [3000, 3000] and even beyond, which makes a mesh unnecessary on most of the surface and especially where we don’t need high resolution.

While if we limit the display volume with the Maple’s view command (view = [x₁..x₂, y₁..y₂, z₁..z₂]), the edges are always smooth regardless of the coordinates system or the type of mesh of the surface to be treated.

And so, the reason I’m writing this message is to ask you why creating trimmed surface with plot3d surface wouldn’t use Maple view’s algorithm to get smooth edges?

Future Alternative Solution:

I also take this opportunity to ask you when would it be possible to update the Maple’s grid option such that the point space will variable in term of surface variable. For example:

plot3d(<x(s,t), y(s,t), z(s,t)>, s = s₁..s₂, t = t₁..t₂, grid = [m(s,t), n(s,t)] )

I am sure that this solution, which for me does not seem to be difficult to implement, could be an alternative to enrich the mesh where we really need it and therefore a better control. What do you think?

Thank you in advance.

Best.

Guy.

https://www.maplesoft.com/applications/view.aspx?SID=3589&view=html

I am trying to export a 3D plot from Maple (2021) in a vector format that can be imported into Adobe Illustrator without too much trouble. The graphic artist says the PDF files are not useful (“at the base of every PDF is an image file, inside layers and layers of clipping paths; not helpful”). “SVG does not appear to produce usable vectors – well, maybe not, but the one you sent me was super difficult to wrangle”. She had hoped that EPS would be useful, but she was unable to open the EPS file I created (not enough memory).

Here is the example that I have been using as I've asked others for help with this question.

restart;
with(plots);
with(plottools);

T := torus([0, 0, 0], 1/2, 1/2);
C0 := spacecurve([cos(t), sin(t), 0], t = 0 .. 2*Pi, color = red, thickness = 9);
C1 := spacecurve([0.5*cos(t), 0.5*sin(t), 0.5], t = 0 .. 2*Pi, color = red, thickness = 9);
C2 := spacecurve([0.5*(1 + cos(t)), 0, 0.5*sin(t)], t = 0 .. Pi, color = blue, thickness = 9);
C3 := spacecurve([0.5*(-1 + cos(t)), 0, 0.5*sin(t)], t = 0 .. Pi, color = blue, thickness = 9);
Fig9510 := display([T, C0, C1, C2], view = [DEFAULT, DEFAULT, 0 .. 1/2], scaling = constrained, transparency = 0.75);

Direct links to the worksheet and the PDF, EPS, and SVG files on DropBox are provide below in the hope that something will be useful to somebody. (MaplePrimes links are provided for the MW and PDF files are also provided - but EPS and SVG files are not permitted.)

1. 3DPlotExample.mw: https://www.dropbox.com/s/mx1hg1ntuqihnu3/3DPlotExample.mw?dl=0
2. Fig9510.pdf: https://www.dropbox.com/s/bnzfqrh060gw84g/Fig9510.pdf?dl=0
3. Fig9510.eps: https://www.dropbox.com/s/h9bjyn0uwm8w5ct/Fig9510.eps?dl=0
4. Fig9510.svg: https://www.dropbox.com/s/u2xfntnqvbhu810/Fig9510.svg?dl=0

This question has been asked for more than ten years. The best solution to has been to use the command-line-interface version of Maple.

1. Is the command-line interface still the best/only option for vector-based graphics output?
2. If so, how do i access the command-line version of Maple 2021 on MacOS?

We consider a triangle ABC, its circumscribed circle (O), of radius R, its inscribed circle (I) of centre I. We designate by α, β, γ the points of contact of BC, CA, AB with the circle (I), by A', B', C' the points of meeting other than A, B, C, of AI, BI, CI with the circle (O), by the media of BC, CA, AB.
.Establish that there is a conic (E), focus I, tangent to βγ, γα, αβ.
My code : 

restart;
with(geometry);
with(plots); _local(gamma);
_EnvHorizontalName := x; _EnvVerticalName := y;
alias(coor = coordinates);
point(A, -5, -5); point(B, 7, -1); point(C, 1, 5);
triangle(ABC, [A, B, C]); circumcircle(_O, ABC, 'centername' = OO); incircle(_I, ABC, 'centername' = Io);
line(lBC, [B, C]); sol := solve({Equation(_I), Equation(lBC)}, {x, y}); point(alpha, subs(sol, x), subs(sol, y));
line(lCA, [C, A]); sol := solve({Equation(_I), Equation(lCA)}, {x, y}); point(beta, subs(sol, x), subs(sol, y));
line(lAB, [A, B]); sol := solve({Equation(_I), Equation(lAB)}, {x, y}); point(gamma, subs(sol, x), subs(sol, y));
line(lAO, [A, OO]); intersection(Ap, lAO, lBC);
line(lBO, [B, OO]); intersection(Bp, lBO, lCA);
line(lCO, [C, OO]); intersection(Cp, lCO, lAB);
midpoint(l, B, C); midpoint(m, A, C); midpoint(n, A, B);
triangle(T, [alpha, beta, gamma]);
dr := draw([ABC(color = blue), _O(color = red), _I(color = magenta), lAO(color = black), lBO(color = black), lCO(color = black), T(color = red), alpha, beta, gamma, Ap, Bp, Cp, l, m, n], printtext = true);
display([dr], axes = normal, scaling = constrained, size = [800, 800]);
How to find the Equation of (E); Thank you.

Why is the minus sign so weak even in the bold font case? My students sometimes miss it in online tests.
How do we make the minus sign bolder?
Thank you!

mapleatha

There seems to be an "issue" when using a indexed name (say x[4]) as the loop index in a seq() mul() or add() command - the indexed name is assigned once the command exits!!

This never(?) happens if the loop index is not an indexed name. A bug??

See the attached which illustrates the issue for the add() command, where x[4] is assigned on exit from add(). The same thing happens if add() is replaced with seq() or mul()

Download aBug.mw

My PC is dual-booted (Win10 and Ubuntu 20.04+KDE). After creating a plot (even the simplest one) and enabling Probe Info as described in  https://www.maplesoft.com/support/help/maple/view.aspx?path=worksheet%2Fplotinterface%2Fpointprobei I do not see tooltip with cursor position. All other tooltips (Palettes, Toolbar etc.) work fine, it is only the probe Info tooltip that does not work. The same plot done while running Maple on Win10 works as expected - tooltip is visible. 

Can someone confirm whether it works for them using Linux? I wonder whether this could be Java-related problem when running on Linux KDE with compositing and using Nvidia driver (e.g. color of tooltip is white on white, or rendering does not work as expected).

I do not remember whether it ever worked on Linux. At this moment I am using Maple2021 but for testing purposes I reinstalled Maple2020 and the problem is the same.

Thanks,

Alex

Hi 

As the titel states: It is possible to create a asymptotic bode plot in maple?

I know how to do a normal bode plot with the DynamicSystem package. But is it possible to get a straight line approximation/ asymptotic bode plot instead?