no. 4
On the mobility and efficiency of mechanical systems
ESAIM: Control, Optimisation and Calculus of Variations, Tome 13 (2007) no. 4, pp. 657-668.

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.

DOI : 10.1051/cocv:2007034
Classification : 37J50, 37K25, 70H33
Mots clés : lagrangian mechanics, efficiency, self-locomotion 
@article{COCV_2007__13_4_657_0,
     author = {Wolansky, Gershon},
     title = {On the mobility and efficiency of mechanical systems},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {657--668},
     publisher = {EDP-Sciences},
     volume = {13},
     number = {4},
     year = {2007},
     doi = {10.1051/cocv:2007034},
     mrnumber = {2351396},
     zbl = {1123.37027},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1051/cocv:2007034/}
}
TY  - JOUR
AU  - Wolansky, Gershon
TI  - On the mobility and efficiency of mechanical systems
JO  - ESAIM: Control, Optimisation and Calculus of Variations
PY  - 2007
SP  - 657
EP  - 668
VL  - 13
IS  - 4
PB  - EDP-Sciences
UR  - http://archive.numdam.org/articles/10.1051/cocv:2007034/
DO  - 10.1051/cocv:2007034
LA  - en
ID  - COCV_2007__13_4_657_0
ER  - 
%0 Journal Article
%A Wolansky, Gershon
%T On the mobility and efficiency of mechanical systems
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 2007
%P 657-668
%V 13
%N 4
%I EDP-Sciences
%U http://archive.numdam.org/articles/10.1051/cocv:2007034/
%R 10.1051/cocv:2007034
%G en
%F COCV_2007__13_4_657_0
Wolansky, Gershon. On the mobility and efficiency of mechanical systems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 13 (2007) no. 4, pp. 657-668. doi : 10.1051/cocv:2007034. http://archive.numdam.org/articles/10.1051/cocv:2007034/

[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). | MR

[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. Mechanica 38 (2003) 505-518. | Zbl

[3] S. Chipot, M. Hastings and D. Kinderlehrer, Transport in a molecular system. ESAIM: M2AN 38 (2004) 1011-1034. | Numdam | Zbl

[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. | Zbl

[5] L.C. Evans, Weak Convergence Methods for Nonlinear Partial Differential Equations. CEMS 74, American Mathematical Society (1990). | MR | Zbl

[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. | Zbl

[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). | MR | Zbl

[10] J. Wisdom, Swimming in sapcetime: Motion by cyclic changes in body shape. Science 299 (2003) 1865-1869.

Cité par Sources :