Abstract
If D’Alembert principle is used on the particles of a rigid body, the principle would state: When a rigid body that is in equilibrium (either static of dynamic) is subject to virtual compatible displacements, the total virtual work of all external forces is zero; and conversely, if the total virtual work of all external forces acting on a rigid body is zero then the body is in equilibrium. (Lanczos 1970).
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Notes
- 1.
Other coordinate systems like polar or any other my result more adequate for particular problems.
- 2.
In strictly mathematical sense, this expression is not the inertial angular momentum conservation. However its solution is the same to the real one provided that the linear momentum equation (Newton’s) is preserved.
- 3.
In the original paper (Kirchhoff 1869) this equation set is presented as 6 (largely more complicated) scalar equations, since they predate the vector notation.
- 4.
This vector expression is being presented in (Meirovitch 1970).
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Olguín Díaz, E. (2019). Dynamics of a Rigid Body. In: 3D Motion of Rigid Bodies. Studies in Systems, Decision and Control, vol 191. Springer, Cham. https://doi.org/10.1007/978-3-030-04275-2_5
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DOI: https://doi.org/10.1007/978-3-030-04275-2_5
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