scholarly journals A generalized virial theorem and the balance of kinetic and potential energies in the semiclassical limit

2010 ◽  
Vol 43 (47) ◽  
pp. 474032
Author(s):  
D R Yafaev
Keyword(s):  
Virial Theorem ◽  
Semiclassical Limit ◽  
Generalized Virial Theorem ◽  
Kinetic And Potential Energies

Lagrangian Mechanics

2019 ◽  
pp. 53-82
Author(s):  
David D. Nolte
Keyword(s):  
Dynamical Systems ◽  
Conservation Laws ◽  
Euler Equations ◽  
Virial Theorem ◽  
Variational Calculus ◽  
Mechanical Action ◽  
Lagrange Equations ◽  
Time Average ◽  
The Difference ◽  
Kinetic And Potential Energies

Dynamical systems follow trajectories for which the mechanical action integrated along the trajectory is an extremum. The action is defined as the time average of the difference between kinetic and potential energies, which is also the time average of the Lagrangian. Once a Lagrangian has been defined for a system, the Euler equations of variational calculus lead to the Euler–Lagrange equations of dynamics. This chapter explores applications of Lagrangians and the use of Lagrange’s undetermined multipliers. Conservation laws, central forces, and the virial theorem are developed and explained.

scholarly journals Generalized virial theorem for the Liénard-type systems

Pramana ◽  
2015 ◽  
Vol 84 (3) ◽  
pp. 373-385 ◽  
Author(s):  
JOSÉ F CARIÑENA ◽  
ANINDYA GHOSE CHOUDHURY ◽  
PARTHA GUHA
Keyword(s):  
Virial Theorem ◽  
Type Systems ◽  
Generalized Virial Theorem

scholarly journals Generalized virial theorem in warped DGP brane-world

2011 ◽  
Vol 84 (2) ◽  
Author(s):  
Malihe Heydari-Fard ◽  
Mohaddese Heydari-Fard
Keyword(s):  
Virial Theorem ◽  
Brane World ◽  
Generalized Virial Theorem

scholarly journals A geometric approach to a generalized virial theorem

2012 ◽  
Vol 45 (39) ◽  
pp. 395210 ◽  
Author(s):  
José F Cariñena ◽  
Fernando Falceto ◽  
Manuel F Rañada
Keyword(s):  
Virial Theorem ◽  
Geometric Approach ◽  
Generalized Virial Theorem

scholarly journals Virial theorem in quasi-coordinates and Lie algebroid formalism

2014 ◽  
Vol 11 (09) ◽  
pp. 1450055 ◽  
Author(s):  
José F. Cariñena ◽  
Irina Gheorghiu ◽  
Eduardo Martínez ◽  
Patrícia Santos
Keyword(s):  
Virial Theorem ◽  
Mechanical Systems ◽  
Geometric Approach ◽  
Point Of View ◽  
Lie Algebroids ◽  
Hamiltonian Mechanics ◽  
Lie Algebroid ◽  
Lagrangian And Hamiltonian Mechanics ◽  
Generalized Virial Theorem

In this paper, the geometric approach to the virial theorem (VT) developed in [J. F. Cariñena, F. Falceto and M. F. Rañada, A geometric approach to a generalized virial theorem, J. Phys. A: Math. Theor. 45 (2012) 395210, 19 pp.] is written in terms of quasi-velocities (see [J. F. Cariñena, J. Nunes da Costa and P. Santos, Quasi-coordinates from the point of view of Lie algebroid structures, J. Phys. A: Math. Theor. 40 (2007) 10031–10048]). A generalization of the VT for mechanical systems on Lie algebroids is also given, using the geometric tools of Lagrangian and Hamiltonian mechanics on the prolongation of the Lie algebroid.

Quantum-mechanical stress and a generalized virial theorem for clusters and solids

1988 ◽  
Vol 37 (14) ◽  
pp. 8167-8178 ◽  
Author(s):  
P. Ziesche ◽  
J. Gräfenstein ◽  
O. H. Nielsen
Keyword(s):  
Mechanical Stress ◽  
Virial Theorem ◽  
Quantum Mechanical ◽  
Generalized Virial Theorem
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