Abstract
This chapter is devoted to Lazare Carnot’s mechanics of impact and to a formulation of a WVL generalized to dynamics. In the first part the mechanics of impact of hard bodies is presented. Through an appropriate definition of virtual velocity and motion (the geometric motion) Carnot succeeds in formulating a generalization of VWL that allows one to evaluate the velocities of a system of hard bodies each of which the initial velocity is known. In the second part his extension to gradually variable forces is presented with the introduction of virtual or real work, named moment of activity, as the fundamental magnitudes of applied mechanics.
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Notes
- 1.
p. 347; pp. 271–296; pp. 299–340.
- 2.
- 3.
p. VII.
- 4.
pp. 120–124.
- 5.
p. 2.
- 6.
pp. 3–5.
- 7.
pp. 46–49.
- 8.
p. 47.
- 9.
p. 14.
- 10.
pp. 15–16.
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pp. 17–18.
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p. 64.
- 13.
pp. 16–17.
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pp. 49–50.
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p. 23.
- 16.
p. 108. English translation from [332], p. 43.
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p. 119.
- 18.
p. 26.
- 19.
p. 130.
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p. 116.
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p. 42.
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pp. 44–45.
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p. 48.
- 24.
Carnot’s theorem is today proved in a few easy steps, based on the property of the inner product between vectors: W 2 = (V + U) · (U + V) = U 2 + V 2 + 2U · V = U 2 + V 2 + 2UV cosZ.
- 25.
pp. 49–50.
- 26.
p. 84.
- 27.
p. 64. Carnot also tries to extend his theory to systems with elasticity. First, he points out that (11.7) also applies to bodies that are not hard, while relation (11.6) is no longer valid. He also proposes an approximate method to deal with the case by introducing a multiplier — it seems invariable over time — of the force of impact F.
- 28.
p. 66.
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p. 73.
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pp. 73–75.
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p. 77.
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p XI.
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p. 2.
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p. 69.
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pp. 82–83.
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p. 114.
- 37.
Carnot wondered what passive forces are, what difference there is between them and active forces. He believed that this is an important issue to which no one has responded, nor even attempted to answer. The distinctive character of the passive forces, for him, is that they can never become actions, while the active forces can act either as active forces or as resistant forces. Those of walls and fixed points are passive forces because they cannot act as active forces.
- 38.
p. 101. The text by Gillispie is presently probably the most exhaustive on a historical analysis of Carnot’s mechanics.
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© 2012 Springer-Verlag Italia
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Capecchi, D. (2012). Lazare Carnot’s mechanics of collision. In: History of Virtual Work Laws. Science Networks. Historical Studies, vol 42. Springer, Milano. https://doi.org/10.1007/978-88-470-2056-6_11
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