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Newtonian Mechanics

In: Differential Equations: Theory and Applications

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  • David Betounes

    (Valdosta State University, Department of Physics, Astronomy and Geosciences)

Abstract

In this chapter we discuss a few aspects of Newtonian mechanics for systems of discrete particles. Such systems are the primary classical examples of systems of differential equations and serve to illustrate many of the concepts that have been developed for the study of systems of DEs. The case for N = 2 particles (the two-body problem) was completely solved, for forces of mutual attraction, in Chapter 2, and here we consider the general N-particle case. The N-body problem has been studied in depth for many centuries, and an enormous body of important and deep results has accrued (cf. [Th 79, p. 176], [W 47, p. 233], and [Wh 65, p. 339]). You should realize however that the general problem (even when the forces are an inverse square law of attraction) is not solvable in closed form, as the N = 2 case and certain special cases of the N = 3 problem are. However, numerical methods are always available and we will see below that they are quite effective in studying the complex motions of a system when the number of particles is not too large.

Suggested Citation

  • David Betounes, 2010. "Newtonian Mechanics," Springer Books, in: Differential Equations: Theory and Applications, chapter 0, pages 371-474, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4419-1163-6_8
    DOI: 10.1007/978-1-4419-1163-6_8
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