Lagrangian and Hamiltonian Mechanics

10.1142/4035 ◽  
1999 ◽  
Author(s):  
M G Calkin
Keyword(s):  
Hamiltonian Mechanics ◽  
Lagrangian And Hamiltonian Mechanics

scholarly journals A SURVEY OF LAGRANGIAN MECHANICS AND CONTROL ON LIE ALGEBROIDS AND GROUPOIDS

2006 ◽  
Vol 03 (03) ◽  
pp. 509-558 ◽  
Author(s):  
JORGE CORTÉS ◽  
MANUEL DE LEÓN ◽  
JUAN C. MARRERO ◽  
D. MARTÍN DE DIEGO ◽  
EDUARDO MARTÍNEZ
Keyword(s):  
Control Systems ◽  
Classical Field Theory ◽  
Nonholonomic Constraints ◽  
Classical Field ◽  
Lie Algebroids ◽  
Hamiltonian Mechanics ◽  
Lagrangian Mechanics ◽  
Geometric Description ◽  
Lagrangian And Hamiltonian Mechanics ◽  
And Control

In this survey, we present a geometric description of Lagrangian and Hamiltonian Mechanics on Lie algebroids. The flexibility of the Lie algebroid formalism allows us to analyze systems subject to nonholonomic constraints, mechanical control systems, Discrete Mechanics and extensions to Classical Field Theory within a single framework. Various examples along the discussion illustrate the soundness of the approach.

Lagrangian and Hamiltonian mechanics

1984 ◽  
pp. 85-103
Author(s):  
B. P. Cowan
Keyword(s):  
Hamiltonian Mechanics ◽  
Lagrangian And Hamiltonian Mechanics

scholarly journals Solved Problems in Lagrangian and Hamiltonian Mechanics

2009 ◽  
Author(s):  
Claude Gignoux ◽  
Bernard Silvestre-Brac
Keyword(s):  
Hamiltonian Mechanics ◽  
Lagrangian And Hamiltonian Mechanics

ϕ-Lagrangian and Hamiltonian mechanics on SO(2)

2012 ◽  
Vol 6 (1) ◽  
pp. 31
Author(s):  
Esmaeil Azizpour
Keyword(s):  
Hamiltonian Mechanics ◽  
Lagrangian And Hamiltonian Mechanics

POTENTIALS OF ARBITRARY FORCES WITH FRACTIONAL DERIVATIVES

2004 ◽  
Vol 19 (17n18) ◽  
pp. 3083-3092 ◽  
Author(s):  
EQAB M. RABEI ◽  
TAREQ S. ALHALHOLY ◽  
AKRAM ROUSAN
Keyword(s):  
Laplace Transform ◽  
General Formula ◽  
Fractional Derivatives ◽  
Fractional Integrals ◽  
Hamiltonian Mechanics ◽  
Dissipative Effects ◽  
Special Cases ◽  
Exact Agreement ◽  
The Laplace Transform ◽  
Lagrangian And Hamiltonian Mechanics

The Laplace transform of fractional integrals and fractional derivatives is used to develop a general formula for determining the potentials of arbitrary forces: conservative and nonconservative in order to introduce dissipative effects (such as friction) into Lagrangian and Hamiltonian mechanics. The results are found to be in exact agreement with Riewe's results of special cases. Illustrative examples are given.

scholarly journals Discrete Lagrangian and Hamiltonian mechanics on Lie groupoids

Nonlinearity ◽  
2006 ◽  
Vol 19 (12) ◽  
pp. 3003-3004 ◽  
Author(s):  
J C Marrero ◽  
D Martín de Diego ◽  
E Martínez
Keyword(s):  
Hamiltonian Mechanics ◽  
Lie Groupoids ◽  
Lagrangian And Hamiltonian Mechanics

Newtonian, Lagrangian and Hamiltonian Mechanics

2021 ◽  
pp. 11-31
Author(s):  
Salvatore Capozziello ◽  
Wladimir-Georges Boskoff
Keyword(s):  
Hamiltonian Mechanics ◽  
Lagrangian And Hamiltonian Mechanics

scholarly journals Transformation properties of the Lagrange function

2008 ◽  
Vol 30 (3) ◽  
pp. 3306.1-3306.8
Author(s):  
Carlo Ferrario ◽  
Arianna Passerini
Keyword(s):  
Equations Of Motion ◽  
Lagrange Function ◽  
Hamiltonian Formalism ◽  
Undergraduate Teaching ◽  
Hamiltonian Mechanics ◽  
Coordinate Transformations ◽  
Lagrangian And Hamiltonian Mechanics ◽  
The Relationship ◽  
Theoretical Mechanics

In the context of the Lagrangian and Hamiltonian mechanics, a generalized theory of coordinate transformations is analyzed. On the basis of such theory, a misconception concerning the superiority of the Hamiltonian formalism with respect to the Lagrangian one is criticized. The consequent discussion introduces the relationship between the classical Hamilton action and the covariance properties of equations of motion, at the level of undergraduate teaching courses in theoretical mechanics.

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