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On a theorem of Chekanov

Emmanuel Ferrand (1997)

Banach Center Publications

A proof of the Chekanov theorem is discussed from a geometric point of view. Similar results in the context of projectivized cotangent bundles are proved. Some applications are given.

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 Σ , χ and M satisfy conditions (11.7) when 𝒬 is a polynomial in γ ˙ , conditions (C)-i.e. (11.8) and (11.7) with 𝒬 0 -are proved to be necessary for treating satisfactorily Σ '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 ( ) z ˙ = F ( t , z , u , u ˙ ) ( m ) with a scalar control u = u ( ) is linear w.r.t. u ˙ iff ( α ) its solution z ( u , ) with given initial conditions (chosen arbitrarily) is continuous w.r.t. u in a certain sense, or iff ( β ) z

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