The Experts below are selected from a list of 5301 Experts worldwide ranked by ideXlab platform
Stanislav D Furta - One of the best experts on this subject based on the ideXlab platform.
-
inversion problem for the Lagrange Theorem on the stability of equilibrium and related problems
2013Co-Authors: V V Kozlov, Stanislav D FurtaAbstract:In this chapter we consider problems that we will solve by a method that we originally used for proving instability in cases where linearized equations alone were insufficient. This first section will serve mostly as an introduction. Here we will outline a range of problems and formulate a number of Theorems on stability for which converse assertions are introduced in the final sections, their proof being based on the construction of asymptotic solutions. In these Theorems the principal stability condition will be the presence of an isolated minimum of some function that plays the role of the potential energy of the system.
-
On some problems of stability of systems with an infinite number of degrees of freedom
Meccanica, 1994Co-Authors: Stanislav D FurtaAbstract:Si considera il problema di stabilità di punti di equilibrio di un pendolo fisico con un filo inestensibile appeso ad esso dal punto di vista del teorema di Lagrange sulla stabilità e sulla sua inversione. Difficoltà specifiche relative allo studio di un sistema meccanico di dimensione infinita sono discusse. Si suggerisce un nuovo metodo per lo studio della stabilità rispetto a due metriche. L'influenza di fenomeni di risonanza sul moto del sistema ridotto (linearizzato) è considerata. The problem of stability of equilibria of a physical pendulum with a nonstretchable thread attached to it is considered from the standpoint of the Lagrange Theorem on stability and its inversion. Specific difficulties which one faces when studying an infinite dimensional mechanical system are discussed. A new approach to the study of stability with respect to two metrics is suggested. The influence of resonant phenomena on the motion of the shortened (linearized) system is considered.
Stephen Simons - One of the best experts on this subject based on the ideXlab platform.
-
Bootstrapping the Mazur--Orlicz--K\"onig Theorem
arXiv: Functional Analysis, 2015Co-Authors: Stephen SimonsAbstract:In this paper, we give some extensions of K\"onig's extension of the Mazur-Orlicz Theorem. These extensions include generalizations of a surprising recent result of Sun Chuanfeng, and generalizations to the product of more than two spaces of the "Hahn-Banach-Lagrange" Theorem.
-
THE HAHN-BANACH-Lagrange Theorem
Optimization, 2007Co-Authors: Stephen SimonsAbstract:This article is about a new version of the Hahn–Banach Theorem, which we will call the “Hahn–Banach–Lagrange Theorem”, since it deals very effectively with certain problems of Lagrange type, as well as giving numerous results in functional analysis, convex analysis, and monotone operator theory. We will discuss several of these results in this article. †Dedicated to Diethard Pallaschke, on the occasion of his 65th birthday.
John E. Prussing - One of the best experts on this subject based on the ideXlab platform.
-
Application of the Euler-Lagrange Theorem
Optimal Control with Aerospace Applications, 2013Co-Authors: James M. Longuski, José J. Guzmán, John E. PrussingAbstract:In this chapter we will look at some applications of the Euler-Lagrange Theorem. The Theorem transforms the Problem of Bolza into a set of differential equations and attendant boundary conditions. In some cases, simple closed-form solutions are available which completely solve the problem. In other cases, numerical methods are required to solve the “two-point boundary-value problem.” In some instances we find that the Euler-Lagrange Theorem does not supply enough conditions to determine the optimal control law. In such cases we appeal to another Theorem (the Weierstrass condition or Minimum Principle, discussed in Chap. 5) to solve the problem.
-
The Euler-Lagrange Theorem
Optimal Control with Aerospace Applications, 2013Co-Authors: James M. Longuski, José J. Guzmán, John E. PrussingAbstract:The brachistochrone problem posed by Johann Bernoulli was a new type of mathematical problem which required a new mathematical approach. Lagrange developed the calculus of variations in which he considered suboptimal paths nearby the optimal one. He then showed that, for arbitrary but infinitesimal variations from the optimal path, the function sought must obey a differential equation now known as the Euler-Lagrange equation.
-
The Weierstrass Condition
Optimal Control with Aerospace Applications, 2013Co-Authors: James M. Longuski, José J. Guzmán, John E. PrussingAbstract:In Chap. 4 we noted that there are optimization problems that cannot be resolved by the Euler-Lagrange Theorem alone. Pontryagin’s Minimum Principle often provides an additional condition that leads to a specific control law and to the solution of the problem. The most general form of the Minimum Principle is stated in Chap. 6 without proof.
James M. Longuski - One of the best experts on this subject based on the ideXlab platform.
-
Application of the Euler-Lagrange Theorem
Optimal Control with Aerospace Applications, 2013Co-Authors: James M. Longuski, José J. Guzmán, John E. PrussingAbstract:In this chapter we will look at some applications of the Euler-Lagrange Theorem. The Theorem transforms the Problem of Bolza into a set of differential equations and attendant boundary conditions. In some cases, simple closed-form solutions are available which completely solve the problem. In other cases, numerical methods are required to solve the “two-point boundary-value problem.” In some instances we find that the Euler-Lagrange Theorem does not supply enough conditions to determine the optimal control law. In such cases we appeal to another Theorem (the Weierstrass condition or Minimum Principle, discussed in Chap. 5) to solve the problem.
-
The Euler-Lagrange Theorem
Optimal Control with Aerospace Applications, 2013Co-Authors: James M. Longuski, José J. Guzmán, John E. PrussingAbstract:The brachistochrone problem posed by Johann Bernoulli was a new type of mathematical problem which required a new mathematical approach. Lagrange developed the calculus of variations in which he considered suboptimal paths nearby the optimal one. He then showed that, for arbitrary but infinitesimal variations from the optimal path, the function sought must obey a differential equation now known as the Euler-Lagrange equation.
-
The Weierstrass Condition
Optimal Control with Aerospace Applications, 2013Co-Authors: James M. Longuski, José J. Guzmán, John E. PrussingAbstract:In Chap. 4 we noted that there are optimization problems that cannot be resolved by the Euler-Lagrange Theorem alone. Pontryagin’s Minimum Principle often provides an additional condition that leads to a specific control law and to the solution of the problem. The most general form of the Minimum Principle is stated in Chap. 6 without proof.
Alexandre Borovik - One of the best experts on this subject based on the ideXlab platform.
-
A note on multivalued groups
Ricerche di Matematica, 2012Co-Authors: Houshang Behravesh, Alexandre BorovikAbstract:Buchstaber (Mosc Math J 6(1):57–84, 2006 ) defined multivalued groups. In this paper we will show that the first isomorphism Theorem and Lagrange Theorem dose not hold for multivalued groups. Finally we define stabilizer of an action and we show that orbit-stabilizer Theorem is not true for multivalued-groups.
