Abstract
In deriving the equations of motion for vertical dynamics, we have seen that either the principle of impulse and momentum (Sect. 4.2) or the principle of virtual displacements, or in other words, the principle of d’Alembert in the version of Lagrange (Sect. 4.2) can be used. For general problems with constraints and preloads, it is often more convenient to use the principle of virtual displacements, even though the choice is also a matter of personal preference.
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Notes
- 1.
Preloads are loads that exist at the beginning of the oscillation process, typically the weight.
- 2.
The moments of inertia \(\Theta _\mathrm{z}\) and \(\Theta _\mathrm{x}\) are equal by symmetry. Therefore, \(\Theta _\mathrm{x} = \Theta _\mathrm{z}\) is always assumed.
- 3.
For example, \(\delta v_\mathrm{xL}\) is the virtual spring deformation of the spring in the x-direction on the left-hand side.
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Knothe, K., Stichel, S. (2017). Derivation of Equations of Motion for Lateral Dynamics. In: Rail Vehicle Dynamics. Springer, Cham. https://doi.org/10.1007/978-3-319-45376-7_9
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DOI: https://doi.org/10.1007/978-3-319-45376-7_9
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