Inverse problem for Lagrangian mechanics

Known as: Helmholtz condition, Douglas theorem, Douglas' theorem

In mathematics, the inverse problem for Lagrangian mechanics is the problem of determining whether a given system of ordinary differential equations…

Papers overview

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2018

In this paper, firstly we investigate conditions under which the action of an operator on a $K$-frame, remain again a $K$-frame…

2012

Based on the Helmholtz conditions for the existence of a Lagrangian, we discuss a new approach to constants of the motion…

2012

The inverse problem of the calculus of variations in a nonholonomic setting is studied. The concept of constraint variationality…

2009

We use Frolicher-Nijenhuis theory to obtain global Helmholtz conditions, expressed in terms of a semi-basic 1-form, that…

2008

2005

We show that a special form of the Furuta inequality is equivalent to an operator equation p—2rn p+2r p—2rn H2mJT (H n+i T)«#2…

2005

Abstract Mechanics is the origin of physics. Almost any physical theory like electrodynamics stems from mechanical explanations…

2004

Based on recent developments in the theory of variational and Hamiltonian control systems by Crouch and van der Schaft, this…

2003

The variational sequence describes the Helmholtz conditions for local variationality in terms of the Helmholtz map, which is…

2002

Variational properties of first order mechanical systems with general non-holonomic constraints are studied. The concept of…