Quantum Theory for Mathematicians pp 19-52 | Cite as

# A First Approach to Classical Mechanics

Chapter

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## Abstract

We begin by considering the motion of a single particle in \({\mathbb{R}}^{1},\) which may be thought of as a particle sliding along a wire, or a particle with motion that just happens to lie in a line. We let where we use a dot over a symbol to denote the derivative of that quantity with respect to the time

*x*(*t*) denote the particle’s position as a function of time. The particle’s velocity is then$$\displaystyle{v(t) :=\dot{ x}(t),}$$

*t*.## Keywords

Angular Momentum Poisson Bracket Kepler Problem Angular Momentum Vector Hamiltonian Vector Field
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## References

- [28].W.G. Kelley, A.C. Petersen,
*The Theory of Differential Equations: Classical and Qualitative (Universitext)*, 2nd edn. (Springer, New York, 2010)Google Scholar - [29].J. Lee,
*Introduction to Smooth Manifolds*, 2nd edn. (Springer, London, 2006)Google Scholar - [44].R.E. Williamson, R.H. Crowell, H.F. Trotter,
*Calculus of Vector Functions*, 3rd edn. (Prentice-Hall, Englewood Cliffs, NJ, 1968)Google Scholar

## Copyright information

© Springer Science+Business Media New York 2013