On the mobility and efficiency of mechanical systems

Gershon Wolansky

ESAIM: Control, Optimisation and Calculus of Variations (2007)

  • Volume: 13, Issue: 4, page 657-668
  • ISSN: 1292-8119

Abstract

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It is shown that self-locomotion is possible for a body in Euclidian space, provided its dynamics corresponds to a non-quadratic Hamiltonian, and that the body contains at least 3 particles. The efficiency of the driver of such a system is defined. The existence of an optimal (most efficient) driver is proved.


How to cite

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Wolansky, Gershon. "On the mobility and efficiency of mechanical systems." ESAIM: Control, Optimisation and Calculus of Variations 13.4 (2007): 657-668. <http://eudml.org/doc/250015>.

@article{Wolansky2007,
abstract = { It is shown that self-locomotion is possible for a body in Euclidian space, provided its dynamics corresponds to a non-quadratic Hamiltonian, and that the body contains at least 3 particles. The efficiency of the driver of such a system is defined. The existence of an optimal (most efficient) driver is proved.
},
author = {Wolansky, Gershon},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Lagrangian mechanics; efficiency; self-locomotion; optimal driver},
language = {eng},
month = {7},
number = {4},
pages = {657-668},
publisher = {EDP Sciences},
title = {On the mobility and efficiency of mechanical systems},
url = {http://eudml.org/doc/250015},
volume = {13},
year = {2007},
}

TY - JOUR
AU - Wolansky, Gershon
TI - On the mobility and efficiency of mechanical systems
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2007/7//
PB - EDP Sciences
VL - 13
IS - 4
SP - 657
EP - 668
AB - It is shown that self-locomotion is possible for a body in Euclidian space, provided its dynamics corresponds to a non-quadratic Hamiltonian, and that the body contains at least 3 particles. The efficiency of the driver of such a system is defined. The existence of an optimal (most efficient) driver is proved.

LA - eng
KW - Lagrangian mechanics; efficiency; self-locomotion; optimal driver
UR - http://eudml.org/doc/250015
ER -

References

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  1. J.E. Avron and O. Kenneth, Swimming in curved space or The Baron and the Cat. Arxiv preprint math-ph/0602053 - arxiv.org (2006).  
  2. D. Chipot, M. Kinderlehrer and M. Kowalczyk, A variational principle for molecular motors, dedicated to piero villagio on the occasion of his 60 birthday. Mechanica38 (2003) 505–518.  Zbl1032.92005
  3. S. Chipot, M. Hastings and D. Kinderlehrer, Transport in a molecular system. ESAIM: M2AN38 (2004) 1011–1034.  Zbl1077.35060
  4. D. Dolbeault, J. Kinderlehrer and M. Kowalczyk, Remarks about the flashing rachet, partial differential equations and inverse problems. Contemp. Math. 362 (2004) 167–175.  Zbl1064.35065
  5. L.C. Evans, Weak Convergence Methods for Nonlinear Partial Differential Equations. CEMS 74, American Mathematical Society (1990).  
  6. O. Gat, J.E. Avron and O. Kenneth, Optimal swimming at low reynolds numbers. Phys. Rev. Lett.93 (2004) 18.  
  7. J.C. Oxtoby, Homeomorphic measures in metric spaces. Proc. Amer. Math. Soc.24 (1970) 419–423.  Zbl0187.00902
  8. R.E. Raspe, The Surprising Adventures of Baron Munchusen. Kessinger Publishing (2004).  
  9. R.M. Wald, General Relativity, Appendix C3. The University of Chicago Press (1984).  
  10. J. Wisdom, Swimming in sapcetime: Motion by cyclic changes in body shape. Science299 (2003) 1865–1869.  

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