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Displaying 21 – 40 of 137

On Axiomatic Foundations Common to Classical Physics and Special Relativity

Aldo Bressan (2005)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

(i) The class of the axiomatic foundations mentioned in the title is called Ax Found; and its structure is treated in the introduction. (ii) This consists of Parts A to G followed by the References. (iii) In [17] Bressan's modal logic is treated in a consciously non-rigorous way. Instead here, as well as Ax Found, it has a rigorous treatment. Such a treatment had been appreciated by the mathematical physicist C. Truesdell in [62]. (iv) In 1953 Truesdell had a remarkable...

On Carnot's theorem in time dependent impulsive mechanics.

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...

On central configurations.

Richard Moeckel (1990)

Mathematische Zeitschrift

On classical dynamics of affinely-rigid bodies subject to the Kirchhoff-Love constraints.

Kovalchuk, Vasyl (2010)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

On classical intrinsically resonant formal perturbation theory

Marcin Moszyński (1995)

Annales de l'I.H.P. Physique théorique

On classical $r$ -matrix for the Kowalevski gyrostat on $so (4)$ .

Komarov, Igor V., Tsiganov, Andrey V. (2006)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

On control problems of minimum time for Lagrangian systems similar to a swing. I. Convexity criteria for sets

Aldo Bressan, Monica Motta (1994)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

One establishes some convexity criteria for sets in $R^{2}$ . They will be applied in a further Note to treat the existence of solutions to minimum time problems for certain Lagrangian systems referred to two coordinates, one of which is used as a control. These problems regard the swing or the ski.

On control problems of minimum time for Lagrangian systems similar to a swing. II Application of convexity criteria to certain minimum time problems

Aldo Bressan, Monica Motta (1994)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

This Note is the Part II of a previous Note with the same title. One refers to holonomic systems $Σ = A ⋃ U$ with two degrees of freedom, where the part $A$ can schemetize a swing or a pair of skis and $U$ schemetizes whom uses $A$ . The behaviour of $U$ is characterized by a coordinate used as a control. Frictions and air resistance are neglected. One considers on $Σ$ minimum time problems and one is interested in the existence of solutions. To this aim one determines a certain structural condition $Γ$ which implies...

On control theory and its applications to certain problems for Lagrangian systems. On hyperimpulsive motions for these. II. Some purely mathematical considerations for hyper-impulsive motions. Applications to Lagrangian systems

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 $\Sigma$ , $\chi$ and $M$ satisfy conditions (11.7) when $\mathcal{Q}$ is a polynomial in $\dot{\gamma}$ , conditions (C)-i.e. (11.8) and (11.7) with $\mathcal{Q}\equiv 0$ -are proved to be necessary for treating satisfactorily $\Sigma$ 's hyper-impulsive motions (in which positions can suffer first order discontinuities)....

On control theory and its applications to certain problems for Lagrangian systems. On hyper-impulsive motions for these. III. Strengthening of the characterizations performed in parts I and II, for Lagrangian systems. An invariance property.

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 $(\mathcal{E})\dot{z}=F(t,z,u,\dot{u})\,(\in\mathbb{R}^{m})$ with a scalar control $u=u(\cdot)$ is linear w.r.t. $\dot{u}$ iff $(\alpha)$ its solution $z(u,\cdot)$ with given initial conditions (chosen arbitrarily) is continuous w.r.t. $u$ in a certain sense, or iff $(\beta)$ $z(u,\cdot)$

On D’Alembert’s Principle

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.

On decomposability of Nambu-Poisson tensor.

Alekseevsky, D., Guha, P. (1996) Acta Mathematica Universitatis Comenianae. New Series

On differential inclusions of velocity hodograph type with Carathéodory conditions on Riemannian manifolds

Yuri E. Gliklikh, Andrei V. Obukhovski (2004) Discussiones Mathematicae, Differential Inclusions, Control and Optimization

We investigate velocity hodograph inclusions for the case of right-hand sides satisfying upper Carathéodory conditions. As an application we obtain an existence theorem for a boundary value problem for second-order differential inclusions on complete Riemannian manifolds with Carathéodory right-hand sides.

On existence and uniqueness of the solution of the equation of motion for constrained mechanical systems.

Udwadia, Firdaus E., Kalaba, Robert E., Nashed, M.Zuhair (1995) Mathematical Problems in Engineering

On Galilean connections and the first jet bundle

James Grant, Bradley Lackey (2012) Open Mathematics

We see how the first jet bundle of curves into affine space can be realized as a homogeneous space of the Galilean group. Cartan connections with this model are precisely the geometric structure of second-order ordinary differential equations under time-preserving transformations - sometimes called KCC-theory. With certain regularity conditions, we show that any such Cartan connection induces “laboratory” coordinate systems, and the geodesic equations in this coordinates form a system of second-order...

Currently displaying 21 – 40 of 137

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Displaying 21 – 40 of 137

On Axiomatic Foundations Common to Classical Physics and Special Relativity

On Carnot's theorem in time dependent impulsive mechanics.

On central configurations.

On classical dynamics of affinely-rigid bodies subject to the Kirchhoff-Love constraints.

On classical intrinsically resonant formal perturbation theory

On classical $r$ -matrix for the Kowalevski gyrostat on $so (4)$ .

On control problems of minimum time for Lagrangian systems similar to a swing. I. Convexity criteria for sets

On control problems of minimum time for Lagrangian systems similar to a swing. II Application of convexity criteria to certain minimum time problems

On control theory and its applications to certain problems for Lagrangian systems. On hyperimpulsive motions for these. II. Some purely mathematical considerations for hyper-impulsive motions. Applications to Lagrangian systems

On control theory and its applications to certain problems for Lagrangian systems. On hyper-impulsive motions for these. III. Strengthening of the characterizations performed in parts I and II, for Lagrangian systems. An invariance property.

On D’Alembert’s Principle

On decomposability of Nambu-Poisson tensor.

On differential inclusions of velocity hodograph type with Carathéodory conditions on Riemannian manifolds

On existence and uniqueness of the solution of the equation of motion for constrained mechanical systems.

On Galilean connections and the first jet bundle

On higher order geometry on anchored vector bundles

On implicit Lagrangian differential systems

On integration factor of a dynamical system.

On integration of the differential equation of central motion, I

On isomorphism of integrable cases of the Euler equations on the bi-Hamiltonian manifolds $e (3)$ and $so (4)$ .

Currently displaying 21 – 40 of 137