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I am trying to implement a simple simulation of a point mass connected to a linear and to an angular spring. I thought this would be very easy, basically just integrating these two equations:

[tex]mr''=-k_l(r-L)-c_lr'[/tex]

[tex]m\theta''=-k_a(\theta-\alpha)-c_a\theta'[/tex]

These are in polar coordinates [tex](r,\theta)[/tex], where [tex]k_l,c_l,L[/tex] are the stiffness, damping coefficient and rest length of the linear spring and [tex]k_a,c_a,\alpha[/tex] - of the angular spring.

It looks like it works correctly but then I realized that it iswrong. For example, with initial conditions [tex]r'(0)=0,r(0)=L[/tex] the point will never change its distance from the origin no matter what the angular speed is, so there is no centrifugal force... This is obvious in hindsight because the two equations are completely independent.

So now I'm stuck and not really sure what I'm missing here. Any help is appreciated.

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# Linear and angular spring simulation

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