Classical Mechanics - Department of Physics and Astronomy

Classical Mechanics - Department of Physics and Astronomy

Classical mechanics, narrowly defined, is the investigation of the motion of systems of particles in Euclidean three-dimensional space, under the influence of specified force laws, with the motion’s evolution determined by Newton’s second law, a second order differential equation. That is, given certain laws determining physical forces, and some boundary conditions on the positions of the particles at some particular times, the problem is to determine the positions of all the particles at all times. We will be discussing motions under specific fundamental laws of great physical importance, such as Coulomb’s law for the electrostatic force between charged particles. We will also discuss laws which are less fundamental, because the motion under them can be solved explicitly, allowing them to serve as very useful models for approximations to more complicated physical situations, or as a testbed for examining concepts in an explicitly evaluatable situation. Techniques suitable for broad classes of force laws will also be developed.



The formalism of Newtonian classical mechanics, together with investigations into the appropriate force laws, provided the basic framework for physics from the time of Newton until the beginning of this century. The systems considered had a wide range of complexity. One might consider a single particle on which the Earth’s gravity acts. But one could also consider systems as the limit of an infinite number of very small particles, with displacements smoothly varying in space, which gives rise to the continuum limit. One example of this is the consideration of transverse waves on a stretched string, in which every point on the string has an associated degree of freedom, its transverse displacement.

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