Titlebook: Analytical Mechanics; Classical, Lagrangia Valter Moretti Textbook 20231st edition The Editor(s) (if applicable) and The Author(s), under e

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Foundations of Lagrangian Mechanics,In this chapter we shall introduce the . of Classical Mechanics. We remind that the presence of constraint reactions with unknown expression typically makes Newton’s equations ., precisely because these forces appear as additional unknowns.

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, Mathematical Introduction to Special Relativity and the Relativistic Lagrangian Formulation,In this chapter we will discuss the mathematical principles underpinning the theory of Special Relativity from a geometrical and axiomatic point of view. The motivation for the axioms, which are based on crucial experimental evidence and the ensuing physical postulates due to Einstein, will be discussed in Complement in Chap. ..

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Balance Equations and First Integrals in Mechanics,nservation laws”. These laws are actually theorems, that follow from the principles of Classical Mechanics stated in Chap. .. They deal in particular with: the linear momentum, the angular momentum and the mechanical energy. We will discuss together the cases of one particle and systems of several particles.

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Advanced Topics in Lagrangian Mechanics,d Theoretical Physics, even in faraway contexts from Classical Mechanics. We will introduce the variational formulation of the Euler-Lagrange equations, the notion of generalised potential and some definitions and results on stability theory.

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Fundamentals of Hamiltonian Mechanics, by W.R.Hamilton and then boosted by several other mathematical physicists until the present day. Apart from the indisputable importance within classical Mathematical Physics, Hamiltonian Mechanics has had a deep influence on the theoretical development of many areas of Physics such as modern . and . at the start of the twentieth century.

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Analytical Mechanics978-3-031-27612-5Series ISSN 2038-5714 Series E-ISSN 2532-3318