Variational nonsmooth mechanics via a projected Hamilton's principle

2012 ◽  
Author(s):  
D. Pekarek ◽  
T. D. Murphey
Keyword(s):  
Hamilton’S Principle ◽  
Hamilton's Principle ◽  
Nonsmooth Mechanics

Dynamic Modeling of Satellite Tether Systems Using Newton’s Laws and Hamilton’s Principle

2007 ◽  
Vol 130 (1) ◽  
Author(s):  
Kalyan K. Mankala ◽  
Sunil K. Agrawal
Keyword(s):  
Dynamic Modeling ◽  
Continuous System ◽  
Variable Length ◽  
Variable Domain ◽  
Dynamic Equations ◽  
Hamilton’S Principle ◽  
Hamilton's Principle ◽  
Newton’S Laws

The objective of this paper is to derive the dynamic equations of a tether as it is deployed or retrieved by a winch on a satellite orbiting around Earth using Newton’s laws and Hamilton’s principle and show the equivalence of the two methods. The main feature of this continuous system is the presence of a variable length domain with discontinuities. Discontinuity is present at the boundary of deployment because of the assumption that the stowed part of the cable is unstretched and the deployed part is not. Developing equations for this variable domain system with discontinuities, specially using Hamilton’s principle, is a nontrivial task and we believe that it has not been adequately addressed in the literature.

Dynamics of 3D Micropolar Gyroelastic Beams

2014 ◽  
Author(s):  
Soroosh Hassanpour ◽  
G. R. Heppler
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Dynamic Modeling ◽  
Dynamic Equations ◽  
Hamilton’S Principle ◽  
The Finite Element Method ◽  
Hamilton's Principle ◽  
Modeling And Analysis ◽  
Element Method

This paper is devoted to the dynamic modeling of micropolar gyroelastic beams and explores some of the modeling and analysis issues related to them. The simplified micropolar beam torsion and bending theories are used to derive the governing dynamic equations of micropolar gyroelastic beams from Hamilton’s principle. Then these equations are solved numerically by utilizing the finite element method and are used to study the spectral and modal behaviour of micropolar gyroelastic beams.

Modified Hamilton's Principle

1973 ◽  
Vol 41 (10) ◽  
pp. 1188-1190 ◽  
Author(s):  
John R. Ray
Keyword(s):  
Hamilton’S Principle ◽  
Hamilton's Principle

scholarly journals Multisymplectic formulation of fluid dynamics using the inverse map

2007 ◽  
Vol 463 (2086) ◽  
pp. 2671-2687 ◽  
Author(s):  
C.J Cotter ◽  
D.D Holm ◽  
P.E Hydon
Keyword(s):  
Fluid Dynamics ◽  
Conservation Laws ◽  
Fluid Particle ◽  
Hamilton’S Principle ◽  
Hamilton's Principle ◽  
Numerical Integrators ◽  
Fluid Particles ◽  
Infinite Set ◽  
Circulation Theorem

We construct multisymplectic formulations of fluid dynamics using the inverse of the Lagrangian path map. This inverse map, the ‘back-to-labels’ map, gives the initial Lagrangian label of the fluid particle that currently occupies each Eulerian position. Explicitly enforcing the condition that the fluid particles carry their labels with the flow in Hamilton's principle leads to our multisymplectic formulation. We use the multisymplectic one-form to obtain conservation laws for energy, momentum and an infinite set of conservation laws arising from the particle relabelling symmetry and leading to Kelvin's circulation theorem. We discuss how multisymplectic numerical integrators naturally arise in this approach.

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