메뉴 건너뛰기




Volumn 98, Issue 2, 2007, Pages 121-144

Lie group variational integrators for the full body problem in orbital mechanics

Author keywords

Full rigid body problem; Lie group method; Symplectic integrator; Variational integrator

Indexed keywords


EID: 34247849138     PISSN: 09232958     EISSN: 15729478     Source Type: Journal    
DOI: 10.1007/s10569-007-9073-x     Document Type: Article
Times cited : (109)

References (26)
  • 2
    • 25844476221 scopus 로고    scopus 로고
    • Efficient Lie-Poisson integrator for secular spin dynamics of rigid bodies
    • Breiter, S., Nesvorný, D., Vokrouhlický, D.: Efficient Lie-Poisson integrator for secular spin dynamics of rigid bodies. Astron. J. 130, 1267-1277 (2005b)
    • (2005) Astron. J , vol.130 , pp. 1267-1277
    • Breiter, S.1    Nesvorný, D.2    Vokrouhlický, D.3
  • 5
    • 45449123467 scopus 로고
    • Lie-Poisson Hamilton-Jacobi theory and Lie-Poisson integrators
    • Ge, Z., Marsden, J.E.: Lie-Poisson Hamilton-Jacobi theory and Lie-Poisson integrators. Phys. Lett. A 133(3), 134-139 (1988)
    • (1988) Phys. Lett. A , vol.133 , Issue.3 , pp. 134-139
    • Ge, Z.1    Marsden, J.E.2
  • 6
    • 34247857857 scopus 로고    scopus 로고
    • Hairer, E.: Backward analysis of numerical integrators and symplectic methods. Ann. Numer. Math. 1, 107-132 scientific computation and differential equations (Auckland, 1993). (1994)
    • Hairer, E.: Backward analysis of numerical integrators and symplectic methods. Ann. Numer. Math. 1, 107-132 scientific computation and differential equations (Auckland, 1993). (1994)
  • 10
    • 0033243778 scopus 로고    scopus 로고
    • Symplectic-energy-momentum preserving variational integrators
    • Kane, C., Marsden, J.E., Ortiz, M.: Symplectic-energy-momentum preserving variational integrators. J. Math. Phys. 40(7), 3353-3371 (1999)
    • (1999) J. Math. Phys , vol.40 , Issue.7 , pp. 3353-3371
    • Kane, C.1    Marsden, J.E.2    Ortiz, M.3
  • 11
    • 24044436529 scopus 로고    scopus 로고
    • Explicit momentum-conserving integrator for dynamics of rigid bodies approximating the midpoint Lie algorithm
    • Krysl, P.: Explicit momentum-conserving integrator for dynamics of rigid bodies approximating the midpoint Lie algorithm. Int. J. Numer. Methods Eng. 63, 2171-2193 (2005)
    • (2005) Int. J. Numer. Methods Eng , vol.63 , pp. 2171-2193
    • Krysl, P.1
  • 12
    • 46449105087 scopus 로고    scopus 로고
    • A Lie group variational integrator for the attitude dynamics of a rigid body with applications to the 3D pendulum
    • Lee, T., Leok, M., McClamroch, N.H.: A Lie group variational integrator for the attitude dynamics of a rigid body with applications to the 3D pendulum. In: Proceedings of the IEEE Conference on Control Applications, pp. 962-967 (2005)
    • (2005) Proceedings of the IEEE Conference on Control Applications , pp. 962-967
    • Lee, T.1    Leok, M.2    McClamroch, N.H.3
  • 13
    • 34247559618 scopus 로고    scopus 로고
    • Lee, T., Leok, M., McClamroch, N.H.: Lie group variational integrators for the full body problem. Comput. Methods App. Mech. Eng. in press (2007)
    • Lee, T., Leok, M., McClamroch, N.H.: Lie group variational integrators for the full body problem. Comput. Methods App. Mech. Eng. in press (2007)
  • 15
    • 3643132297 scopus 로고
    • Reduction, relative equilibria and potential in the two rigid bodies problem
    • Maciejewski, A.J.: Reduction, relative equilibria and potential in the two rigid bodies problem. Celestial Mech. Dyn. Astr. 63, 1-28 (1995)
    • (1995) Celestial Mech. Dyn. Astr , vol.63 , pp. 1-28
    • Maciejewski, A.J.1
  • 17
    • 0033228880 scopus 로고    scopus 로고
    • Discrete Euler-Poincaré and Lie-Poisson equations
    • Marsden, J.E., Pekarsky, S., Shkoller, S.: Discrete Euler-Poincaré and Lie-Poisson equations. Nonlinearity 12, 1647-1662 (1999)
    • (1999) Nonlinearity , vol.12 , pp. 1647-1662
    • Marsden, J.E.1    Pekarsky, S.2    Shkoller, S.3
  • 18
    • 0007071020 scopus 로고    scopus 로고
    • Symmetry reduction of discrete Lagrangian mechanics on Lie groups
    • Marsden, J.E., Pekarsky, S., Shkoller, S.: Symmetry reduction of discrete Lagrangian mechanics on Lie groups. J. Geom. Phys. 36, 139-150 (2000)
    • (2000) J. Geom. Phys , vol.36 , pp. 139-150
    • Marsden, J.E.1    Pekarsky, S.2    Shkoller, S.3
  • 19
    • 84959193128 scopus 로고    scopus 로고
    • Discrete mechanics and variational integrators
    • Marsden, J.E., West, M.: Discrete mechanics and variational integrators. Acta Numerica 10, 357-514 (2001)
    • (2001) Acta Numerica , vol.10 , pp. 357-514
    • Marsden, J.E.1    West, M.2
  • 20
    • 0000008977 scopus 로고
    • Discrete versions of some classical integrable systems and factorization of matrix polynomials
    • Moser, J., Veselov, A.P.: Discrete versions of some classical integrable systems and factorization of matrix polynomials. Commun. Math. Phys. 139, 217-243 (1991)
    • (1991) Commun. Math. Phys , vol.139 , pp. 217-243
    • Moser, J.1    Veselov, A.P.2
  • 21
    • 0036375860 scopus 로고    scopus 로고
    • Stability in the Full Two-Body problem
    • Scheeres, D.J.: Stability in the Full Two-Body problem. Celestial Mech. Dyn. Astr. 83, 155-169 (2002)
    • (2002) Celestial Mech. Dyn. Astr , vol.83 , pp. 155-169
    • Scheeres, D.J.1
  • 22
    • 0026939543 scopus 로고
    • Exact energy-momentum conserving algorithms and symplectic schemes for nonlinear dynamics
    • Simo, J.C., Tarnow, N., Wong, K.K.: Exact energy-momentum conserving algorithms and symplectic schemes for nonlinear dynamics. Comput. Methods Appl. Mech. Eng. 100, 63-116 (1992)
    • (1992) Comput. Methods Appl. Mech. Eng , vol.100 , pp. 63-116
    • Simo, J.C.1    Tarnow, N.2    Wong, K.K.3
  • 23
    • 4243635078 scopus 로고
    • Lie-Poisson integrator for rigid body dynamics in the solar system
    • Touma, J., Wisdom, J.: Lie-Poisson integrator for rigid body dynamics in the solar system. Astron. J. 107, 1189-1202 (1994)
    • (1994) Astron. J , vol.107 , pp. 1189-1202
    • Touma, J.1    Wisdom, J.2
  • 24
    • 0031210701 scopus 로고    scopus 로고
    • Mechanical integrator derived from a discrete variational principle
    • Wendlandt, J.M., Marsden, J.E.: Mechanical integrator derived from a discrete variational principle. Physica D 106, 223-246 (1997)
    • (1997) Physica D , vol.106 , pp. 223-246
    • Wendlandt, J.M.1    Marsden, J.E.2
  • 25
    • 23844555307 scopus 로고    scopus 로고
    • Werner, R.A., Scheeres, D.J.: Mutual potential of homogenous polyhedra. Celest. Mech. and Dyn. Astr. 91, 337-349 (2005)
    • Werner, R.A., Scheeres, D.J.: Mutual potential of homogenous polyhedra. Celest. Mech. and Dyn. Astr. 91, 337-349 (2005)
  • 26
    • 0001005075 scopus 로고
    • Construction of high order symplectic integrators
    • Yoshida, H.: Construction of high order symplectic integrators. Phys. Lett. A 150, 262-268 (1990)
    • (1990) Phys. Lett. A , vol.150 , pp. 262-268
    • Yoshida, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.