Dirac structures in Lagrangian mechanics Part I: Implicit Lagrangian systems

[1]  Gabriel Kron,et al.  Tensor analysis of networks , 1967 .

[2]  Paul Adrien Maurice Dirac,et al.  Generalized Hamiltonian dynamics , 1958, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[3]  C Wansdronk On the mechanism of hearing. , 1961 .

[4]  Gabriel Kron,et al.  Diakoptics : the piecewise solution of large-scale systems , 1963 .

[5]  J. K. Moser,et al.  A theory of nonlinear networks. I , 1964 .

[6]  Ralph Abraham,et al.  Foundations Of Mechanics , 2019 .

[7]  Lagrangian systems on manifolds, I , 1970 .

[8]  Frank Harary,et al.  Mathematical aspects of electrical network analysis , 1971 .

[9]  S. Smale On the mathematical foundations of electrical circuit theory , 1972 .

[10]  I. Neĭmark,et al.  Dynamics of Nonholonomic Systems , 1972 .

[11]  Alan S. Perelson,et al.  Chemical reaction dynamics part II: Reaction networks , 1974 .

[12]  G. Oster,et al.  Chemical reaction dynamics , 1974 .

[13]  L. Chua,et al.  A theory of nonenergic N‐ports , 1977 .

[14]  W. M. Tulczyjew The Legendre transformation , 1977 .

[15]  S. Sastry,et al.  Jump behavior of circuits and systems , 1981, CDC 1981.

[16]  Ray Skinner,et al.  Generalized Hamiltonian dynamics. I. Formulation on T*Q⊕TQ , 1983 .

[17]  R. Weber,et al.  Hamiltonian systems with constraints and their meaning in mechanics , 1986 .

[18]  Irene Ya. Dorfman,et al.  Dirac structures of integrable evolution equations , 1987 .

[19]  Leon O. Chua,et al.  Linear and nonlinear circuits , 1987 .

[20]  T. Courant Tangent dirac structures , 1990 .

[21]  J. Koiller Reduction of some classical non-holonomic systems with symmetry , 1992 .

[22]  A. Schaft,et al.  An intrinsic Hamiltonian formulation of the dynamics of LC-circuits , 1995 .

[23]  van der Arjan Schaft,et al.  On the Hamiltonian Formulation of Nonholonomic Mechanical Systems , 1994 .

[24]  J. Marsden,et al.  Introduction to mechanics and symmetry , 1994 .

[25]  A. Schaft,et al.  The Hamiltonian formulation of energy conserving physical systems with external ports , 1995 .

[26]  L. D. Faddeev,et al.  Lagrangian Mechanics in Invariant Form , 1995 .

[27]  P. Krishnaprasad,et al.  Nonholonomic mechanical systems with symmetry , 1996 .

[28]  Jerrold E. Marsden,et al.  The Hamiltonian and Lagrangian approaches to the dynamics of nonholonomic systems , 1997 .

[29]  Darryl D. Holm,et al.  The Maxwell–Vlasov equations in Euler–Poincaré form , 1998, chao-dyn/9801016.

[30]  A. J. van der Schaft,et al.  Implicit Hamiltonian Systems with Symmetry , 1998 .

[31]  Jerrold E. Marsden,et al.  Poisson reduction for nonholonomic mechanical systems with symmetry , 1998 .

[32]  A. Schaft,et al.  On Representations and Integrability of Mathematical Structures in Energy-Conserving Physical Systems , 1999 .

[33]  Arjan van der Schaft,et al.  Symmetry and reduction in implicit generalized Hamiltonian systems , 1999 .

[34]  Jerrold E. Marsden,et al.  Lagrangian Reduction by Stages , 2001 .

[35]  Sonia Martínez,et al.  Geometric Description of Vakonomic and Nonholonomic Dynamics. Comparison of Solutions , 2002, SIAM J. Control. Optim..

[36]  Jerrold E. Marsden,et al.  Variational integrators for degenerate Lagrangians, with application to point vortices , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[37]  Naomi Ehrich Leonard,et al.  The equivalence of controlled lagrangian and controlled hamiltonian systems , 2002 .

[38]  A. Bloch,et al.  Nonholonomic Mechanics and Control , 2004, IEEE Transactions on Automatic Control.

[39]  Critical manifolds and stability in Hamiltonian systems with non-holonomic constraints , 2003, math-ph/0302017.

[40]  Jerrold E. Marsden,et al.  Reduction of Controlled Lagrangian and Hamiltonian Systems with Symmetry , 2004, SIAM J. Control. Optim..

[41]  Tudor S. Ratiu,et al.  Singular reduction of implicit Hamiltonian systems , 2003, math/0303022.

[42]  Dirk Aeyels,et al.  A Novel Variational Method for Deriving Lagrangian and Hamiltonian Models of Inductor-Capacitor Circuits , 2004, SIAM Rev..