integration: if the force depends on the velocity

[samibouziri]

Hello,

for the exercice 2 to test the integration function we have to generate a force that keeps the boids at a fixed distance of the center. Thus this force will have to depend not only on the position of the boid but also on the velocity. the issue is that in the assignment the force only depends on the position. while the only solution for the Explicit Euler and Symplectic Euler cases is to add v_n as an argument of the force, the Explicit midpoint case is more tricky as we can either add v_n or v_n+1/2 as the argument of the force. So do you have a hint on how to add the velocity as the argument of the force ?

Thanks

[ydual]

For the circular motion, I don't think you need a velocity-dependent force. If you want a velocity-dependent force somewhere later in the exercise, v_n is fine to use.

[liyuesolo]

Yes, you don't need a velocity-dependent force to maintain circular motion.

[samibouziri]

well to maintain a circular motion you need a centrifugal force which depend on the velocity. we can assume that the norm of the velocity is constant but that won't be the case if we integrate numerically.

[liyuesolo]

Maybe let's think of a similar problem and see if it makes sense to you. Do you need a velocity-dependent force to implement Hooke's spring which also aims to preserve the distance between two end points?

[Sibsoon]

If I would implement a hooke's spring I would expect to know the spring constant and the deformation value with it's sign. This implied that we make up a number for k and use the knowledge of the original distance. Or did I misunderstand something?

[liyuesolo]

that's right. You would need a penalty coefficient k, and the original distance is known from your initialization.

[Memphis99]

But is it ok if we use velocities to get the centripetal forces and it works fine? Or we can't use them?

[liyuesolo]

For this exercise please use a position dependent force