Abstract
A general procedure for obtaining the exact control forces to be exerted on a mechanical system to maintain constraints is introduced in this paper. It is illustrated through a simple example. The discussion extends to Nature's choice of control forces and its relation to the general control forces.
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References
Bellman, R.,Introduction to the Mathematical Theory of Control Processes, Vol. 1, Academic Press, New York, New York, 1967.
Bellman, R., andDreyfus, S.,Applied Dynamic Programming, Princeton University Press, Princeton, New Jersey, 1962.
Athans, M., andFalb, P.,Optimal Control, McGraw-Hill Book Company, New York, New York, 1966.
Sage, A.,Optimum Systems Control, Prentice-Hall, Englewood Cliffs, New Jersey, 1968.
Bryson, A., andHo, Y. C.,Applied Optimal Control, Blaisdell Publishing Company, Waltham, Massachusetts, 1969.
Udwadia, F., andKalaba, R.,New Directions in the Control of Nonlinear Mechanical Systems, Mechanics and Control, Edited by R. Guttalu, Plenum Press, New York, New York, 1964.
Kalaba, R., Udwadia, F., Xu, R., andItiki, C.,The Equivalence of Lagrange's Equations of Motion of the First Kind and the Generalized Inverse Form, Nonlinear World, Vol. 2, 1995.
Kalaba, R., Udwadia, F., andXu, R.,Constrained Motion Revisited, Applied Mathematics and Computation, Vol. 7, pp. 67–76, 1995.
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Kalaba, R., Xu, R. On the exact control of mechanical systems. J Optim Theory Appl 87, 349–357 (1995). https://doi.org/10.1007/BF02192568
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DOI: https://doi.org/10.1007/BF02192568