Kinetic energy and Lyapunov stability of equilibria of natural Lagrangian systems

Equadiff 99 ◽  
2000 ◽  
pp. 1155-1157
Author(s):  
Maria Letizia Bertotti ◽  
Sergey V. Bolotin
Keyword(s):  
Kinetic Energy ◽  
Lyapunov Stability ◽  
Lagrangian Systems ◽  
Stability Of Equilibria

scholarly journals ROUTH REDUCTION FOR SINGULAR LAGRANGIANS

2010 ◽  
Vol 07 (08) ◽  
pp. 1451-1489 ◽  
Author(s):  
BAVO LANGEROCK ◽  
MARCO CASTRILLÓN LÓPEZ
Keyword(s):  
Kinetic Energy ◽  
Original System ◽  
Regularity Conditions ◽  
Lagrangian Systems ◽  
Lagrange Equations ◽  
Reduction Procedure ◽  
Momentum Map ◽  
Routh Reduction ◽  
Regular Value ◽  
Singular Lagrangians

This paper concerns the Routh reduction procedure for Lagrangians systems with symmetry. It differs from the existing results on geometric Routh reduction in the fact that no regularity conditions on either the Lagrangian L or the momentum map JL are required apart from the momentum being a regular value of JL. The main results of this paper are: the description of a general Routh reduction procedure that preserves the Euler–Lagrange nature of the original system and the presentation of a presymplectic framework for Routh reduced systems. In addition, we provide a detailed description and interpretation of the Euler–Lagrange equations for the reduced system. The proposed procedure includes Lagrangian systems with a non-positively definite kinetic energy metric.

scholarly journals Mechanics of floating bodies

2021 ◽  
Vol 477 (2255) ◽  
Author(s):  
Robert Beig ◽  
Bernd G. Schmidt
Keyword(s):  
Incompressible Fluid ◽  
Mechanical System ◽  
Lyapunov Stability ◽  
Rigid Bodies ◽  
Equilibrium Theory ◽  
Constant Density ◽  
Floating Bodies ◽  
Stability Of Equilibria

We introduce and study the mechanical system which describes the dynamics and statics of rigid bodies of constant density floating in a calm incompressible fluid. Since much of the standard equilibrium theory, starting with Archimedes, allows bodies with vertices and edges, we assume the bodies to be convex and take care not to assume more regularity than that implied by convexity. One main result is the (Lyapunov) stability of equilibria satisfying a condition equivalent to the standard ‘metacentric’ criterion.

Dependence of the joint configuration on the dynamic immobility fulcrum

2019 ◽  
pp. 108-114
Author(s):  
A. D. Kozlov ◽  
Yu. P. Potekhina
Keyword(s):  
Kinetic Energy ◽  
Convex Surface ◽  
The Other ◽  
Concave Surface ◽  
Joint Configuration ◽  
Articular Surfaces

Although joints with synovial cavities and articular surfaces are very variable, they all have one common peculiarity. In most cases, one of the articular surfaces is concave, whereas the other one is convex. During the formation of a joint, the epiphysis, which has less kinetic energy during the movements in the joint, forms a convex surface, whereas large kinetic energy forms the epiphysis with a concave surface. Basing on this concept, the analysis of the structure of the joints, allows to determine forces involved into their formation, and to identify the general patterns of the formation of the skeleton.

Sign in / Sign up

Export Citation Format

Share Document