Abstract
After introducing the needed defining properties of a N-particle system (such as the center of mass, motion of the center of mass and relative motion with respect to the center of mass, total kinetic energy, force, angular momentum etc.), together with the notions introduced in the previous chapter, and with a little guidance, along this chapter, one will be able to prove many related theorems and deduce interesting results for such systems. Among others the reader will prove König’s theorems as an exercise, energy, momentum and angular momentum conservation, and also analyse simple systems of two particles with their peculiarities. Systems with variable mass will also be treated in this chapter together with related exercises.
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Notes
- 1.
We could have defined this reference system with different orientation of the axes, however, we are not interested in adding further complications, as they would be irrelevant in this chapter.
- 2.
If one doubts about the following result, a simple way of intuitively understand it is to consider a simple potential such as \(U_{ij} = \sqrt{ ( \mathbf {r}_i - \mathbf {r}_j )^2 }\), and check that (5.41) holds true.
- 3.
Again, if one has any problem in following the calculations presented here for a generic potential \(U_{ij}(|\mathbf {r}_i-\mathbf {r}_j|)\) one should use a simple case, such as \(U_{ij} = \sqrt{(\mathbf {r}_i - \mathbf {r}_j)^2}\) in order to understand these results more intuitively.
- 4.
This is not Quantum Mechanics!
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). Systems of Particles and Variable Mass. In: Lectures in Classical Mechanics. Undergraduate Lecture Notes in Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-38585-9_5
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DOI: https://doi.org/10.1007/978-3-030-38585-9_5
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