Titlebook: An Introduction to Hamiltonian Mechanics; Gerardo F. Torres del Castillo Textbook 2018 Springer Nature Switzerland AG 2018 inertia tensor.

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Some Applications of the Lagrangian Formalism,As we have seen in the preceding chapter, the equations of motion of a mechanical system subject to holonomic constraints, with forces derivable from a potential, can be expressed in terms of a single function.

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The Hamiltonian Formalism,In this chapter it is shown that, for a regular Lagrangian, the Lagrange equations can be translated into a set of first-order ODEs, known as the Hamilton, or canonical, equations, which turn out to be more useful than the Lagrange equations, as we shall see in this chapter and in the following ones.

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Canonical Transformations,One of the main reasons why the Hamiltonian formalism is more powerful than the Lagrangian formalism is that the set of coordinate transformations that leave invariant the form of the Hamilton equations is much broader than the set of coordinate transformations that leave invariant the form of the Lagrange equations.

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An Introduction to Hamiltonian Mechanics978-3-319-95225-3Series ISSN 1019-6242 Series E-ISSN 2296-4894

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https://doi.org/10.1007/978-3-319-95225-3inertia tensor; Poisson bracket; Hamiltonian mechanics; canonical transformations; rigid bodies; Liouvill

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978-3-030-06997-1Springer Nature Switzerland AG 2018

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https://doi.org/10.1007/978-3-662-41368-5nt particles such that the distances between them are constant. Even though, in essence, this example is similar to those already considered, the expression of the kinetic energy of a rigid body involves a more elaborate process and the definition of a new object (the inertia tensor)

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Textbook 2018cs like variational symmetries, canonoid transformations, and geometrical optics that are usually omitted from an introductory classical mechanics course. For students with only a basic knowledge of mathematics and physics, this book makes those results accessible through worked-out examples and wel