On a “mysterious” case of a quadratic Hamiltonian.
Sakovich, Sergei (2006)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
M. Adler (1978/1979)
Inventiones mathematicae
Stefano Pasquero (2005)
Extracta Mathematicae
We show that the validity of the Carnot's theorem about the kinetic energy balance for a mechanical system subject to an inert impulsive kinetic constraint, once correctly framed in the time dependent geometric environment for Impulsive Mechanics given by the left and right jet bundles of the space-time bundle N, is strictly related to the frame of reference used to describe the system and then it is not an intrinsic property of the mechanical system itself. We analyze in details the class of frames...
Kovalchuk, Vasyl (2010)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
Marcin Moszyński (1995)
Annales de l'I.H.P. Physique théorique
Aldo Bressan (1988)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
See Summary in Note I. First, on the basis of some results in [2] or [5]-such as Lemmas 8.1 and 10.1-the general (mathematical) theorems on controllizability proved in Note I are quickly applied to (mechanic) Lagrangian systems. Second, in case , and satisfy conditions (11.7) when is a polynomial in , conditions (C)-i.e. (11.8) and (11.7) with -are proved to be necessary for treating satisfactorily 's hyper-impulsive motions (in which positions can suffer first order discontinuities)....
Aldo Bressan (1988)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
In [1] I and II various equivalence theorems are proved; e.g. an ODE with a scalar control is linear w.r.t. iff its solution with given initial conditions (chosen arbitrarily) is continuous w.r.t. in a certain sense, or iff
Larry M. Bates, James M. Nester (2011)
Communications in Mathematics
A formulation of the D’Alembert principle as the orthogonal projection of the acceleration onto an affine plane determined by nonlinear nonholonomic constraints is given. Consequences of this formulation for the equations of motion are discussed in the context of several examples, together with the attendant singular reduction theory.
Alekseevsky, D., Guha, P. (1996)
Acta Mathematica Universitatis Comenianae. New Series
Udwadia, Firdaus E., Kalaba, Robert E., Nashed, M.Zuhair (1995)
Mathematical Problems in Engineering
S. Janeczko (2000)
Annales Polonici Mathematici
Let (P,ω) be a symplectic manifold. We find an integrability condition for an implicit differential system D' which is formed by a Lagrangian submanifold in the canonical symplectic tangent bundle (TP,ὡ).
Eugene Leimanis (1982)
Rendiconti del Seminario Matematico della Università di Padova
Tsyganov, A.V. (2004)
Zapiski Nauchnykh Seminarov POMI
Franco Rampazzo (1988)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
Let be a constrained mechanical system locally referred to state coordinates . Let be an assigned trajectory for the coordinates and let be a scalar function of the time, to be thought as a control. In [4] one considers the control system , which is parametrized by the coordinates and is obtained from by adding the time-dependent, holonomic constraints . More generally, one can consider a vector-valued control which is directly identified with . If one denotes the momenta conjugate...
Paulette Libermann (2000)
Banach Center Publications
We give different notions of Liouville forms, generalized Liouville forms and vertical Liouville forms with respect to a locally trivial fibration π:E → M. These notions are linked with those of semi-basic forms and vertical forms. We study the infinitesimal automorphisms of these forms; we also investigate the relations with momentum maps.
Aldo Bressan, Marco Favretti (1992)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
This Note is the continuation of a previous paper with the same title. Here (Part II) we show that for every choice of the sequence , 's trajectory after the instant tends in a certain natural sense, as , to a certain geodesic of , with origin at . Incidentally is independent of the choice of applied forces in a neighbourhood of arbitrarily prefixed.
Aldo Bressan, Marco Favretti (1991)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
In this Note (which will be followed by a second) we consider a Lagrangian system (possibly without any Lagrangian function) referred to coordinates , , with to be used as a control, and precisely to add to a frictionless constraint of the type . Let 's (frictionless) constraints be represented by the manifold generally moving in Hertz's space. We also consider an instant (to be used for certain limit discontinuity-properties), a point of , a value for 's momentum conjugate...
Irtegov, Valentin D., Titorenko, Tatyana N. (2006)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
Bambusi, Dario, Gaeta, Giuseppe (2002)
Mathematical Physics Electronic Journal [electronic only]
Prykarpatsky, Anatoliy K., Taneri, Ufuk, Samoylenko, Valeriy (2001)
Applied Mathematics E-Notes [electronic only]