Mechanics is the study of rigid body motion. There are 2 levels on which one may enter classical mechanics.

  1. Newton's laws.
  2. Lagrangian and Hamiltonian mechanics

The first is great for one-dimensional motion and non-relativistic planetary motion.  The second is much more powerful.  The generalized coordinates and canonical equation of motion allow derivation of complex system much more efficiently than using Newton's laws.  It is also in the second formulation in which you would come across the D'albert principle, "the sum of the differences between the forces acting on a system and the time derivatives of the momenta of the system itself along any virtual displacement consistent with the constraints of the system, is zero".

Here are a few of the more fundamental problems in classical mechanics:

  1. Static forces and torques - Ladder against a wall solution
  2. 1D kinematics - Parked Nissan GTR solution
  3. Rotational Motion - Freestyle skier flipping into a tuc position solution
  4. Harmonic Motion - Damped driven oscillator solution
  5. 2D Kinematics - Airplane Bomb solution
  6. Non-conservative forces - Friction of box on an incline solution
  7. Collisions - Bullet into block attached to spring solution
  8. Gravity - Conical intersections of incoming asteroid solutions
  9. Non-linearity - Pendulum starting from very high solution
  10. Air Drag - Homerun in Colorado vs. Houston solution

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