-
Previous Article
Andoyer's variables and phases in the free rigid body
- JGM Home
- This Issue
- Next Article
Aspects of reduction and transformation of Lagrangian systems with symmetry
1. | Department of Mathematics, Ghent University, Krijgslaan 281 S22, B9000 Ghent, Belgium, Belgium |
2. | Belgian Institute for Space Aeronomy, Ringlaan 3, B1180 Brussels, Belgium |
References:
[1] |
R. Abraham and J. E. Marsden, Foundations of Mechanics,, The Benjamin/Cummings Publishing Company, (1978).
|
[2] |
M. Crampin and T. Mestdag, Routh's procedure for non-Abelian symmetry groups,, J. Math. Phys., 49 (2008).
doi: 10.1063/1.2885077. |
[3] |
M. J. Gotay, J. M. Nester and G. Hinds, Presymplectic manifolds and the Dirac-Bergmann theory of constraints,, J. Math. Phys., 19 (1978), 2388.
doi: 10.1063/1.523597. |
[4] |
M. J. Gotay and J. M. Nester, Presymplectic Lagrangian systems I: The constraint algorithm and the equivalence problem,, Ann. Inst. Henri Poincaré, 30 (1979), 129.
|
[5] |
S. M. Jalnapurkar and J. E. Marsden, Reduction of Hamilton's variational principle,, Dynamics and Stability of Systems, 15 (2000), 287.
doi: 10.1080/713603744. |
[6] |
S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, volume I and II,, Interscience Publishers, (1963).
|
[7] |
B. Langerock, E. G. Andrés and F. Cantrijn, Routh reduction and the class of magnetic Lagrangian systems,, Journal Of Mathematical Physics, 53 (2012).
doi: 10.1063/1.4723841. |
[8] |
B. Langerock, F. Cantrijn and J. Vankerschaver, Routhian reduction for quasi-invariant Lagrangians,, J. Math. Phys., 51 (2010).
doi: 10.1063/1.3277181. |
[9] |
B. Langerock and M. C. Lopéz, Routhian reduction for singular Lagrangians,, J. Geom. Meth. Mod. Phys., 7 (2010), 1451.
doi: 10.1142/S0219887810004907. |
[10] |
B. Langerock, T. Mestdag and J. Vankerschaver, Routh reduction by stages,, SIGMA Symmetry Integrability Geom. Methods Appl., 7 (2011).
doi: 10.3842/SIGMA.2011.109. |
[11] |
J. E. Marsden, Lectures on Mechanics,, Cambridge University Press, (1992).
|
[12] |
J. E. Marsden, G. Misiołek, J. P. Ortega, M. Perlmutter and T. S. Ratiu, Hamiltonian Reduction by Stages,, volume 1913 of Lecture Notes in Mathematics. Springer, (1913).
|
[13] |
J. E. Marsden, T. S. Ratiu and J. Scheurle, Reduction theory and the Lagrange-Routh equations,, J. Math. Phys., 41 (2000), 3379.
doi: 10.1063/1.533317. |
[14] |
J. E. Marsden and J. Scheurle, Lagrangian reduction and the double spherical pendulum,, Z. Angew. Math. Phys., 44 (1993), 17.
doi: 10.1007/BF00914351. |
[15] |
P. Morando and S. Sammarco, Variational problems with symmetries: A Pfaffian system approach,, Acta Appl. Math., 120 (2012), 255.
doi: 10.1007/s10440-012-9720-4. |
[16] |
R. W. Sharpe, Differential Geometry,, volume 166 of Graduate Texts in Mathematics. Springer-Verlag, (1997).
|
show all references
References:
[1] |
R. Abraham and J. E. Marsden, Foundations of Mechanics,, The Benjamin/Cummings Publishing Company, (1978).
|
[2] |
M. Crampin and T. Mestdag, Routh's procedure for non-Abelian symmetry groups,, J. Math. Phys., 49 (2008).
doi: 10.1063/1.2885077. |
[3] |
M. J. Gotay, J. M. Nester and G. Hinds, Presymplectic manifolds and the Dirac-Bergmann theory of constraints,, J. Math. Phys., 19 (1978), 2388.
doi: 10.1063/1.523597. |
[4] |
M. J. Gotay and J. M. Nester, Presymplectic Lagrangian systems I: The constraint algorithm and the equivalence problem,, Ann. Inst. Henri Poincaré, 30 (1979), 129.
|
[5] |
S. M. Jalnapurkar and J. E. Marsden, Reduction of Hamilton's variational principle,, Dynamics and Stability of Systems, 15 (2000), 287.
doi: 10.1080/713603744. |
[6] |
S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, volume I and II,, Interscience Publishers, (1963).
|
[7] |
B. Langerock, E. G. Andrés and F. Cantrijn, Routh reduction and the class of magnetic Lagrangian systems,, Journal Of Mathematical Physics, 53 (2012).
doi: 10.1063/1.4723841. |
[8] |
B. Langerock, F. Cantrijn and J. Vankerschaver, Routhian reduction for quasi-invariant Lagrangians,, J. Math. Phys., 51 (2010).
doi: 10.1063/1.3277181. |
[9] |
B. Langerock and M. C. Lopéz, Routhian reduction for singular Lagrangians,, J. Geom. Meth. Mod. Phys., 7 (2010), 1451.
doi: 10.1142/S0219887810004907. |
[10] |
B. Langerock, T. Mestdag and J. Vankerschaver, Routh reduction by stages,, SIGMA Symmetry Integrability Geom. Methods Appl., 7 (2011).
doi: 10.3842/SIGMA.2011.109. |
[11] |
J. E. Marsden, Lectures on Mechanics,, Cambridge University Press, (1992).
|
[12] |
J. E. Marsden, G. Misiołek, J. P. Ortega, M. Perlmutter and T. S. Ratiu, Hamiltonian Reduction by Stages,, volume 1913 of Lecture Notes in Mathematics. Springer, (1913).
|
[13] |
J. E. Marsden, T. S. Ratiu and J. Scheurle, Reduction theory and the Lagrange-Routh equations,, J. Math. Phys., 41 (2000), 3379.
doi: 10.1063/1.533317. |
[14] |
J. E. Marsden and J. Scheurle, Lagrangian reduction and the double spherical pendulum,, Z. Angew. Math. Phys., 44 (1993), 17.
doi: 10.1007/BF00914351. |
[15] |
P. Morando and S. Sammarco, Variational problems with symmetries: A Pfaffian system approach,, Acta Appl. Math., 120 (2012), 255.
doi: 10.1007/s10440-012-9720-4. |
[16] |
R. W. Sharpe, Differential Geometry,, volume 166 of Graduate Texts in Mathematics. Springer-Verlag, (1997).
|
[1] |
Huy Dinh, Harbir Antil, Yanlai Chen, Elena Cherkaev, Akil Narayan. Model reduction for fractional elliptic problems using Kato's formula. Mathematical Control & Related Fields, 2021 doi: 10.3934/mcrf.2021004 |
[2] |
Peter Benner, Jens Saak, M. Monir Uddin. Balancing based model reduction for structured index-2 unstable descriptor systems with application to flow control. Numerical Algebra, Control & Optimization, 2016, 6 (1) : 1-20. doi: 10.3934/naco.2016.6.1 |
[3] |
Yuri Chekanov, Felix Schlenk. Notes on monotone Lagrangian twist tori. Electronic Research Announcements, 2010, 17: 104-121. doi: 10.3934/era.2010.17.104 |
2019 Impact Factor: 0.649
Tools
Metrics
Other articles
by authors
[Back to Top]