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Relative periodic solutions of the $ n $-vortex problem on the sphere
Improving E. Cartan considerations on the invariance of nonholonomic mechanics
1. | Universidade de Lisboa, Instituto Superior Técnico, Center for Mathematical Analysis, Geometry and Dynamical Systems, Av. Rovisco Pais, 1049-001 Lisbon, Portugal |
2. | Universidade de São Paulo, Instituto de Matemática e Estatística, Departamento de Matemática Aplicada, Rua do Matão, 1010, 05508-090 São Paulo, Brazil |
3. | Universidade de São Paulo, Instituto de Matemática e Estatística, Departamento de Matemática, Rua do Matão, 1010, 05508-090 São Paulo, Brazil |
This paper concerns an intrinsic formulation of nonholonomic mechanics. Our point of departure is the paper [
References:
[1] |
A. Bakša,
The geometrization of the motion of certain nonholonomic systems, Mat. Vesnik, 12 (1975), 233-240.
|
[2] |
D. I. Barrett, R. Biggs, C. C. Remsing and O. Rossi,
Invariant nonholonomic Riemannian structures on three-dimensional Lie groups, J. Geom. Mech., 8 (2016), 139-167.
doi: 10.3934/jgm.2016001. |
[3] |
É. Cartan, Sur la represéntation géométrique des systmes matériels non holonomes, in Proc Int Congr Math, 4, Bologna, 1928, 253–261. |
[4] |
V. Dragović and B. Gajić,
The Wagner curvature tensor in nonholonomic mechanics, Regul. Chaotic Dyn., 8 (2003), 105-123.
doi: 10.1070/RD2003v008n01ABEH000229. |
[5] |
K. Ehlers and J. Koiller,
Cartan meets Chaplygin, Theoretical and Applied Mechanics, 46 (2019), 15-46.
doi: 10.2298/TAM190116006E. |
[6] |
J. Koiller, P. R. Rodrigues and P. Pitanga, Non-holonomic connections following Élie Cartan, Anais da Academia Brasileira de Cincias, 73 (2001), 165–190, http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652001000200003&nrm=iso.
doi: 10.1590/S0001-37652001000200003. |
[7] |
W. M. Oliva, Geometric Mechanics, vol. 1798 of Lecture Notes in Mathematics, Springer-Verlag, 2002.
doi: 10.1007/b84214. |
[8] |
J. N. Tavares,
About Cartan geometrization of non-holonomic mechanics, J. Geom. Phys., 45 (2003), 1-23.
doi: 10.1016/S0393-0440(02)00118-3. |
[9] |
G. Terra,
The parallel derivative, Revista Matemática Contemporânea, 29 (2005), 157-170.
|
show all references
References:
[1] |
A. Bakša,
The geometrization of the motion of certain nonholonomic systems, Mat. Vesnik, 12 (1975), 233-240.
|
[2] |
D. I. Barrett, R. Biggs, C. C. Remsing and O. Rossi,
Invariant nonholonomic Riemannian structures on three-dimensional Lie groups, J. Geom. Mech., 8 (2016), 139-167.
doi: 10.3934/jgm.2016001. |
[3] |
É. Cartan, Sur la represéntation géométrique des systmes matériels non holonomes, in Proc Int Congr Math, 4, Bologna, 1928, 253–261. |
[4] |
V. Dragović and B. Gajić,
The Wagner curvature tensor in nonholonomic mechanics, Regul. Chaotic Dyn., 8 (2003), 105-123.
doi: 10.1070/RD2003v008n01ABEH000229. |
[5] |
K. Ehlers and J. Koiller,
Cartan meets Chaplygin, Theoretical and Applied Mechanics, 46 (2019), 15-46.
doi: 10.2298/TAM190116006E. |
[6] |
J. Koiller, P. R. Rodrigues and P. Pitanga, Non-holonomic connections following Élie Cartan, Anais da Academia Brasileira de Cincias, 73 (2001), 165–190, http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652001000200003&nrm=iso.
doi: 10.1590/S0001-37652001000200003. |
[7] |
W. M. Oliva, Geometric Mechanics, vol. 1798 of Lecture Notes in Mathematics, Springer-Verlag, 2002.
doi: 10.1007/b84214. |
[8] |
J. N. Tavares,
About Cartan geometrization of non-holonomic mechanics, J. Geom. Phys., 45 (2003), 1-23.
doi: 10.1016/S0393-0440(02)00118-3. |
[9] |
G. Terra,
The parallel derivative, Revista Matemática Contemporânea, 29 (2005), 157-170.
|
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