I'm wondering whether conservation laws are sufficient to imply equations of motions. Specifically:
1) In classical mechanics of point particles, are conservation of energy, conservation of momentum and conservation of angular momentum enough to imply the dynamics? Stated equivalently, given a particle trajectory in configuration space which is not a solution of the equation of motion, does that trajectory necessarily violate the conservation laws?
2) Same question about classical field theory.
3) Same question about point particle quantum mechanics.
4) Same question about quantum field theory.
I'm aware that my question isn't well defined, yet I'm very interested in your answers...