CosmoLearning Physics. Classical Mechanics. John Baez Here are some course notes and homework problems for a mathematics graduate course on classical mechanics.
There are two versions of the course: The second course reviews a lot of basic differential geometry. But, if you'd like to study these courses on your own and don't feel comfortable with manifolds, vector fields, differential forms and vector bundles, you might try the following texts, in rough order of increasing sophistication: Gregory L. Classical mechanics. Diagram of orbital motion of a satellite around the earth, showing perpendicular velocity and acceleration (force) vectors.
In physics, classical mechanics and quantum mechanics are the two major sub-fields of mechanics. Classical mechanics is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces. Notes on Special Relativity.