implement prismaticJoint physics

Question

I'm trying to implement my own physics for an app I'm making in C++, OpenframeWorks. I'm currently using Box2D but I don't need collision detection so I want something much lighter.

I have a world with gravity and a dynamic object with movement constrained by a prismatic joint of an arbitrary length at an arbitrary angle, attached to a static object. Friction is simulated using the joint motor.

I've looked at

Resources for 2d game physics

But everything here seems to focus on building complete physics engines which I don't need to do. Could anyone point me in the right direction for the maths on this?

Answer 1

You just need to separate the force of gravity into two components; Along the Prismatic Joint Axis, and anything else. (See Free body diagrams)

This is easily achieved with the vector dot product between the gravity vector and axis vector. If you first scale the axis vector to length 1, the result of the dot product will be the force along the axis.

To translate the force into acceleration, you just need to divide by the mass of the moving object.

Answer 2

If Box2D has what you want, I'd recommend you reconsider your "lighter" requirement. Unless you can quantify the harm caused by using a library with a few more bytes, I'd say that the benefit will outweigh the cost of you writing it for yourself.

If you have a good understanding of the physics, and want to learn how to do it, by all means go ahead. If not, use what someone more knowledgeable than you has provided and forget the size of the library.