Noether symmetries of discrete nonholonomic dynamical systems

2009 ◽  
Vol 373 (4) ◽  
pp. 409-412 ◽  
Author(s):  
Jing-Li Fu ◽  
Ben-Yong Chen ◽  
Li-Qun Chen
Keyword(s):  
Dynamical Systems ◽  
Noether Symmetries ◽  
Nonholonomic Dynamical Systems

Dynamical systems: Approximate Lagrangians and Noether symmetries

2019 ◽  
Vol 16 (10) ◽  
pp. 1950160 ◽  
Author(s):  
Sameerah Jamal
Keyword(s):  
Riemannian Manifold ◽  
Dynamical Systems ◽  
Variational Principle ◽  
Kinetic Energy ◽  
Equations Of Motion ◽  
Noether Symmetry ◽  
Noether Symmetries ◽  
Geometric Conditions ◽  
Finite Dimensional ◽  
Second Order Equations

We determine the approximate Noether point symmetries of the variational principle characterizing second-order equations of motion of a particle in a (finite-dimensional) Riemannian manifold. In particular, the Lagrangian comprises of kinetic energy and a potential [Formula: see text], perturbed to [Formula: see text]. We establish a convenient system of approximate geometric conditions that suffices for the computation of approximate Noether symmetry vectors and moreover, simplifies the problem of the effect of higher orders of the perturbation. The general results are applied to several practical problems of interest and we find extra Noether symmetries at [Formula: see text].

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