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Motion of Nonholonomous Rheonomous Systems in the Lagrangian Formalism

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DOI: 10.4236/jamp.2015.33043    5,062 Downloads   5,514 Views   Citations
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ABSTRACT

The main purpose of the paper consists in illustrating a procedure for expressing the equations of motion for a general time-dependent constrained system. Constraints are both of geometrical and differential type. The use of quasi-velocities as variables of the mathematical problem opens the possibility of incorporating some remarkable and classic cases of equations of motion. Afterwards, the scheme of equations is implemented for a pair of substantial examples, which are presented in a double version, acting either as a scleronomic system and as a rheonomic system.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Talamucci, F. (2015) Motion of Nonholonomous Rheonomous Systems in the Lagrangian Formalism. Journal of Applied Mathematics and Physics, 3, 295-309. doi: 10.4236/jamp.2015.33043.

References

[1] Poincare, H. (1901) Sur une forme nouvelle des èquations de la mechanique. Comptes Rendus de l’Academie des Sciences, 132, 369-371.
[2] Gantmacher, F.R. (1975) Lectures in Analytical Mechanics. MIR.
[3] Maruskin, J.M. and Bloch, A.M. (2011) The Boltzman-Hamel Equations for the Optimal Control of Mechanical Systems with Nonholonomic Constraints. International Journal of Robust and Nonlinear Control, 21, 373-386.
http://dx.doi.org/10.1002/rnc.1598
[4] Cameron, J.M. and Book, W.J. (1997) Modeling Mechanisms with Nonholonomic Joints Using the Boltzmann-Hamel Equations. Journal International Journal of Robotics Research, 16, 47-59.
http://dx.doi.org/10.1177/027836499701600104
[5] Talamucci, F. (2014) The Lagrangian Method for a Basic Bicycle. Journal of Applied Mathematics and Physics, 2, 46-60.
[6] Levi, M. (2014) Bike Tracks, Quasi-Magnetic Forces, and the Schrodinger Equation. SIAM News, 47.
[7] Zenkov, V., Bloch, A.M. and Mardsen, J.E. (2002) Stabilization of the Unicycle with Rider. Systems and Control Letters, 46, 293-302.
http://dx.doi.org/10.1016/S0167-6911(01)00187-6
[8] Bloch, A.M., Krishnaprasad, P.S., Mardsen, J.E. and Murray, R. (1996) Nonholonomic Mechanical Systems with Symmetry. Archive for Rational Mechanics and Analysis, 136, 21-99.
http://dx.doi.org/10.1007/BF02199365
[9] Bloch, A.M., Mardsen, J.E. and Zenkov, D.V. (2009) Quasivelocities and Symmetries in Non-Holonomic Systems. Dynamical Systems, 24, 187-222.
http://dx.doi.org/10.1080/14689360802609344

  
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