I am playing around with an ellipse, which rotates in 3D.
In its own coordinate system A, its equation of course is
x**2/a**2 + y**2/b**2 + z**2/c**2 = 1
A rotates relative to N, the generalized coordinates are q1, q2, q3,
dq1/dt = u1, etc.
I express the rotated ellipse in N, by using A.variable_map(N), now the
coordinates are, say, N_x, N_y, N_z.
Using sympy.solve I solve the ellipse equation for N_y, I get two
solutions, of which I take the one I need, so, say, I get
N_y = f(N_x, N_z, q1, d2, d3, a, b, c,…)
I want the speed of N_y, so I write:
Speed_N_y = f(…..).diff(t)
Now my problem starts:
In Speed_N_y, there are terms like Derivative(q1(t), t), and same for q2,
q3.
Of course, these terms are u1, u2, u3, but I cannot find a way to replace
Derivative(q1(t), t) with u1, etc.
I tried Speed_N_y.subs({Derivative(q1(t), t): u2}) but this did not work.
I tried Speed_N_y.subs({q1.diff(t): u1}) also this did not work.
I also tried to get rid of these Derivative terms by writing
NY_lam = lambdify( …, Speed_N_y, {‚Derivative(q1(t), t)‘: u1})
This did not give an error - but also did not accomplish anything.
Of course, when I try to lambdify my Speed_N_y and then try to evaluate it
numerically the problems come up, as this Derivative(q1(t), t) is unknown.
Any help is GREATLY appreciated! Thanks!
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