Abstract
We shall treat momentum conservation as a consequence of Newtonian dynamics, despite the fact that it can be deduced from the symmetry considerations (space homogeneity property) in a more sophisticated formalism. The center of mass of a system of particles is a related notion which will be introduced here. We are going to show how the problem of the system of two interacting particles can be reduced to the dynamics of a single particle with reduced mass in a central field.
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Notes
- 1.
A remarkable exception is the electromagnetic force between two moving charges [23]. The completely consistent consideration of this type of interaction can be done only in the scope of the Theory of Relativity (Relativistic Electrodynamics). Therefore, the complete discussion of electromagnetic interactions is not possible in the present book.
- 2.
This is, actually, not infinitely far from the modern quantum understanding of vacuum.
- 3.
The equations set and initial data is called Cauchy’s problem, in honor of nineteenth-century French mathematician, A.-L. Cauchy, who made great contributions in Mathematics and Mechanics.
- 4.
The situation can be more complicated for the forces depending on velocities of the two particles, such as magnetic force. The consistent treatment of this case is possible only within relativistic electrodynamics, but the final output is in agreement with Eq. (4.21).
References
L.D. Landau, E.M. Lifshitz, The Classical Theory of Fields. Course of Theoretical Physics Series, vol. 2
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Shapiro, I.L., de Berredo-Peixoto, G. (2013). Conservation of Momentum. In: Lecture Notes on Newtonian Mechanics. Undergraduate Lecture Notes in Physics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7825-6_4
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DOI: https://doi.org/10.1007/978-1-4614-7825-6_4
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