Abstract
After some brief historical comments, we start this chapter by introducing the Lorentz transformations from basic principles and present some relevant examples for a better conceptual understanding of the underlying phenomena. We reformulate the Newtonian equations of motion in order to obtain their Relativistic Lorentz-invariant formulation. We analyse and comment upon the Newtonian limit \(c\rightarrow \infty \) in all cases. In parallel we give a tensor formulation of all equations. This chapter is therefore intended to introduce all readers to the realm of Special Relativity, step by step, but also to give a more complete vision to a more advanced reader that is already familiar with the subject.
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Notes
- 1.
Some authors use a different metric i.e., a different definition of \(\varDelta s^2\), which is \(\varDelta s^2 = -c\, \varDelta t^2 + \varDelta l^2\) and therefore, the following considerations in terms of the sign of \(\varDelta s^2\) will be the opposite.
- 2.
As we have also mentioned, other type of transformations such as parity or time-reversal that fall into the Lorentz group category, shall not be treated here.
- 3.
Up to constant space-time translations (which leave v and dt invariant).
- 4.
Some authors define the rest mass as \(m_0\) and \(m\equiv \gamma m_0\), which is somehow a dynamical mass. This is not going to be our case.
Further Reading
J.V. José, E.J. Saletan, Classical Dynamics: A Contemporary Approach. Cambridge University Press
S.T. Thornton, J.B. Marion, Classical Dynamics of Particles and Systems
H. Goldstein, C. Poole, J. Safko, Classical Mechanics, 3rd edn. Addison Wesley
J.R. Taylor, Classical Mechanics
D.T. Greenwood, Classical Dynamics. Prentice-Hall Inc.
D. Kleppner, R. Kolenkow, An Introduction to Mechanics
C. Lanczos, The Variational Principles of Mechanics. Dover Publications Inc.
W. Greiner, Classical Mechanics: Systems of Particles and Hamiltonian Dynamics. Springer
H.C. Corben, P. Stehle, Classical Mechanics, 2nd edn. Dover Publications Inc.
T.W.B. Kibble, F.H. Berkshire, Classical Mechanics. Imperial College Press
M.G. Calkin, Lagrangian and Hamiltonian Mechanics
A.J. French, M.G. Ebison, Introduction to Classical Mechanics
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Ilisie, V. (2020). Special Theory of Relativity. In: Lectures in Classical Mechanics. Undergraduate Lecture Notes in Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-38585-9_11
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DOI: https://doi.org/10.1007/978-3-030-38585-9_11
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