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#### Surbhi Gupta

from sympy import *

import numpy as np

from sympy import symbols

def deriv(x,t):

a = array(x)

for i in range(0,len(x)):

temp = x

a

a

*= temp[0].diff(t)*

return a

def matrixmult (A, B):

C = [[0 for row in range(len(A))] for col in range(len(B[0]))]

for i in range(len(A)):

for j in range(len(B[0])):

for k in range(len(B)):

Creturn a

def matrixmult (A, B):

C = [[0 for row in range(len(A))] for col in range(len(B[0]))]

for i in range(len(A)):

for j in range(len(B[0])):

for k in range(len(B)):

C

*[j] += A**[k]*B[k][j]*

return C

l1,l2,m1,m2,t = symbols('l1,l2,m1,m2,t')

g = 10

th1 = Function('th1')(t)

th2 = Function('th2')(t)

th1dot = Derivative(th1, t)

th2dot = Derivative(th2, t)

x1 = array([[l1*sin(th1)], [-l1*cos(th1)]])

x2 = x1 + array([[l2*sin(th1 + th2)], [-l2*cos(th1 + th2)]])

x1dot = deriv(x1, t)

x2dot = x1dot + deriv(x2, t)

temp1 = matrixmult(x1dot.T,x1dot)

temp2 = matrixmult(x2dot.T, x2dot)

kin = (1/2.0)*m1*temp1[0][0] + (1/2.0)*m2*temp2[0][0]

pot = -m1*g*l1*cos(th1) -m2*g*(l1*cos(th1) + l2*cos(th1+th2))

L = kin - pot

e = lambdify((t, l1, l2, m1, m2, th1, th2), L)

all other commands of above code run with no error. but as soon as I give last command (the lambdify 1) I get a syntax error. I think that is because I m using th1 and th2 as Function of t. Can anyone help me on how to solve this?return C

l1,l2,m1,m2,t = symbols('l1,l2,m1,m2,t')

g = 10

th1 = Function('th1')(t)

th2 = Function('th2')(t)

th1dot = Derivative(th1, t)

th2dot = Derivative(th2, t)

x1 = array([[l1*sin(th1)], [-l1*cos(th1)]])

x2 = x1 + array([[l2*sin(th1 + th2)], [-l2*cos(th1 + th2)]])

x1dot = deriv(x1, t)

x2dot = x1dot + deriv(x2, t)

temp1 = matrixmult(x1dot.T,x1dot)

temp2 = matrixmult(x2dot.T, x2dot)

kin = (1/2.0)*m1*temp1[0][0] + (1/2.0)*m2*temp2[0][0]

pot = -m1*g*l1*cos(th1) -m2*g*(l1*cos(th1) + l2*cos(th1+th2))

L = kin - pot

e = lambdify((t, l1, l2, m1, m2, th1, th2), L)

all other commands of above code run with no error. but as soon as I give last command (the lambdify 1) I get a syntax error. I think that is because I m using th1 and th2 as Function of t. Can anyone help me on how to solve this?