#!/usr/bin/env python
# coding: utf-8

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import sympy as sm
import sympy.physics.mechanics as me
me.init_vprinting()


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theta, beta, alpha, l = me.dynamicsymbols('theta, beta, alpha, l')
A, B, C, D = sm.symbols('A, B, C, D', cls=me.ReferenceFrame)


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B.orient_axis(A, theta, A.z)
C.orient_axis(B, beta, -B.x)
D.orient_axis(C, alpha, C.z)


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r = l*D.x
r


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r.express(C)


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r.express(B)


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r.express(A)


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r.dot(C.x).diff(alpha)


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r.dot(C.y).diff(alpha)


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r_alpha_C = r.dot(C.x).diff(alpha)*C.x + r.dot(C.y).diff(alpha)*C.y
r_alpha_C


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r.diff(alpha, C).express(C).simplify()


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theta, beta, alpha, l


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t = me.dynamicsymbols._t


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theta.diff(t)


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r


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r.diff(t, D)


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r.diff(t, A).simplify()


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r.dt(A)


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r.dt(D)


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q = t*A.y
q


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q.dt(A).dt(B)


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q.dt(B).dt(A)