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By Homer Reid
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Extra resources for Solutions to Problems in Goldstein, Classical Mechanics, Second Edition
Example text
Rockafellar, (Kluwer, Amsterdam, 2004) ISBN 978-0-387-29196-3 (print) 978-0-387-29195-6 (on line) 6. M. Frémond, Collisions, Edizioni del Dipartimento di Ingegneria Civile, Università di Roma “Tor Vergata”, (2007). ISBN 978-88-6296-000-7 7. E. Dimnet, Mouvement et collisions de solides rigides et déformables, thèse de l’École nationale des Ponts et Chaussées (2002) Chapter 10 Summary of the Abstract Setting to get the Equations of Motion Abstract The abstract setting to get the equations of motion from the principle of virtual work is describe.
The external forces are abstract concepts, they are elements of the dual space V ∗ . Their work is defined for any V ∈ V˜ where V˜ is the space of the special bounded variation functions with respect to time with value in V. The internal forces are also abstract concepts: they are elements of the dual space ˜ They have neither power nor D∗ . Their work is defined for any D(V ) with V ∈ V. , with D(R) = 0. Both linear space V and deformation operator D are chosen by the engineer. They are not imposed by any mechanical axiom.
Chapter 14 Three Balls on a Plane Abstract The equations of motion of a system made of three balls and a plane are derived. They describe the motion of billiard balls and of balls of the pétanque Provencal game. The three balls and the plane are the system. We assume the plane is very massive and remains immobile. Thus its velocity is null. We may think of three billiard balls or balls of the pétanque Provencal game, [1]. The balls can loose contact with the plane. 1 The System and the Velocities The system is made of the three balls Bn (t), n = 1, 2, 3 and the plane.