Abstract
The second axiom of Newton implies, that the time development of the motion of a point particle or a system of point particles can be calculated, if the forces acting on the particle are known. Besides the fact that the solution of the equations of motion is not necessarily a simple matter, difficulties can arise from different quarters. It is possible that the forces (in the form of a force field or as a function of time or …) are not known explicitly. The motion can be restricted by constraints, which are expressed in the form of geometrical conditions. A simple example of this kind of restriction is the motion on an inclined plane. The pressure, which an object (a mass point) exerts on the surface of the plane, generates a counter pressure which compensates in part the effect of gravitation. This constraining force can be determined by simple means in the case of the inclined plane.
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References
Chapter 10 in H. Goldstein, C.P. Poole, J.L. Safko: ’Classical Mechanics’ (Addison and Wesley, Baltimore, 2001)
Chapters 2.35 to 2.37 in F. Scheck: ’Mechanics’ (Springer Verlag, Heidelberg, 1999)
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© 2010 Springer-Verlag Berlin Heidelberg
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Dreizler, R.M., Lüdde, C.S. (2010). General Formulation of the Mechanics of Point Particles. In: Theoretical Mechanics. Graduate Texts in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11138-9_5
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DOI: https://doi.org/10.1007/978-3-642-11138-9_5
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