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Formalism of classical mechanics underlies a number of powerful mathematical methods that are widely used in theoretical and mathematical physics. This book considers the basics facts of Lagrangian and Hamiltonian mechanics, as well as related topics, such as canonical transformations, integral invariants, potential motion in geometric setting, symmetries, the Noether theorem and systems with constraints. While in some cases the formalism is developed beyond the traditional level adopted in the standard textbooks on classical mechanics, only elementary mathematical methods are used in the...

We construct non-relativistic and relativistic non-Grassmann spinning particles on the ground of oldest idea about spin as "intrinsic angular momentum." Spin degrees of freedom live on a fiber bundle with a base parameterized by the inner angular-momentum coordinates. In the relativistic case, configuration space of the spin degrees of freedom is anti-de Sitter space. This produces both gamma-matrices and Lorentz generators in the course of quantization. Canonical quantization of the model implies the Dirac equation. We present the detailed analysis of both the Lagrangian and the Hamiltonian...

This book presents the dynamics of spinning bodies, the most confusing topic in Classical Mechanics, using both Lagrangian and Hamiltonian formulations. Choosing the variational problem as a sole starting point, it treats the rigid body as a system of particles with holonomic constraints within the standard methods of classical mechanics, eliminating the need for additional postulates. All basic quantities, equations, and integrals of motion are derived systematically. The rotation matrix, central to the formalism, is the main focus. The reader should find this approach more simple,...

This account of the fundamentals of Hamiltonian mechanics also covers related topics such as integral invariants and the Noether theorem. With just the elementary mathematical methods used for exposition, the book is suitable for novices as well as graduates.