# Variational principles

Chapter

## Abstract

In this chapter we show that the motions of a newtonian potential system are extremals of a variational principle, “Hamilton’s principle of least action.”

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## References

- 26.We should specify the class of curves oh which φ is defined and the linear space which contains
*h*. One could assume, for example, that both spaces consist of the infinitely differentiable functions.Google Scholar - 27.Or even for any infinitely differentiable function
*h*.Google Scholar - 28.If it exists.Google Scholar
- 29.One can easily see that this is the theory of “Clairaut’s equation.”Google Scholar
- 30.In practice this convex function will often be a positive definite quadratic form.Google Scholar
- 31.For this it is sufficient, for example, that the level sets of
*H*be compact.Google Scholar - 32.Cf, for example, the book: Halmos,
*Lectures on Ergodic Theory*, 1956 (Mathematical Society of Japan. Publications. No. 3).Google Scholar - 33.A set
*A*is dense in*B*if there is a point of*A*in every neighborhood of every point of*B*.Google Scholar - 34.The direct product of the sets
*A*,*B*,... is the set of points (*a*,*b*,...), with*a*∈*A*,*b*∈*B*,....Google Scholar

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