朴素
发表于 2025-3-23 10:20:10
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.
dagger
发表于 2025-3-23 15:02:33
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.
使人入神
发表于 2025-3-23 19:31:53
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.
Fantasy
发表于 2025-3-23 23:36:55
An Introduction to Hamiltonian Mechanics978-3-319-95225-3Series ISSN 1019-6242 Series E-ISSN 2296-4894
防锈
发表于 2025-3-24 05:08:28
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comely
发表于 2025-3-24 08:47:50
https://doi.org/10.1007/978-3-319-95225-3inertia tensor; Poisson bracket; Hamiltonian mechanics; canonical transformations; rigid bodies; Liouvill
可能性
发表于 2025-3-24 10:46:25
978-3-030-06997-1Springer Nature Switzerland AG 2018
侧面左右
发表于 2025-3-24 15:04:10
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)
使显得不重要
发表于 2025-3-24 23:02:59
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预知
发表于 2025-3-25 02:55:09
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