Connection of first integrals with particular solutions of the nonsimultaneous variational equations for nonholonomic systems

2005 ◽  
Vol 32 (6) ◽  
pp. 628-635 ◽  
Author(s):  
Hong-Bin Zhang ◽  
Li-Qun Chen
Keyword(s):  
Nonholonomic Systems ◽  
First Integrals ◽  
Variational Equations ◽  
Particular Solutions

First integrals of the discrete nonconservative and nonholonomic systems

2005 ◽  
Vol 14 (2) ◽  
pp. 238-243 ◽  
Author(s):  
Zhang Hong-Bin ◽  
Chen Li-Qun ◽  
Liu Rong-Wan
Keyword(s):  
Nonholonomic Systems ◽  
First Integrals

scholarly journals Moving energies as first integrals of nonholonomic systems with affine constraints

Nonlinearity ◽  
2018 ◽  
Vol 31 (3) ◽  
pp. 755-782 ◽  
Author(s):  
Francesco Fassò ◽  
Luis C García-Naranjo ◽  
Nicola Sansonetto
Keyword(s):  
Nonholonomic Systems ◽  
First Integrals ◽  
Affine Constraints

scholarly journals The problem of first integral of nonholonomic systems

2001 ◽  
Vol 23 (1) ◽  
pp. 51-64
Author(s):  
Do Sanh
Keyword(s):  
Nonholonomic System ◽  
Nonholonomic Constraint ◽  
First Integral ◽  
Nonholonomic Systems ◽  
First Integrals

In this paper, the problem of first integrals of a nonholonomic system is discussed. The aim of this work is concentra.ted on finding the condition for existence of first integrals. The obtained results are applied for the construction of linear and quadratic integrals of nonholonomic systems. It obtains two important affirmations; they are: Any first integral could be treated as a particular nonholonomic constraint and contrarily, any nonholonomic constraint could be regarded as a first integral of the nonholonomic system.

scholarly journals THE CARTAN FORM FOR CONSTRAINED LAGRANGIAN SYSTEMS AND THE NONHOLONOMIC NOETHER THEOREM

2011 ◽  
Vol 08 (04) ◽  
pp. 897-923 ◽  
Author(s):  
M. CRAMPIN ◽  
T. MESTDAG
Keyword(s):  
Nonholonomic Constraints ◽  
Nonholonomic Systems ◽  
First Integrals ◽  
Lagrangian Systems ◽  
Noether Theorem ◽  
Cartan Form ◽  
General Relations ◽  
Riemannian Submanifolds ◽  
Form Approach

This paper deals with conservation laws for mechanical systems with nonholonomic constraints. It uses a Lagrangian formulation of nonholonomic systems and a Cartan form approach. We present what we believe to be the most general relations between symmetries and first integrals. We discuss the so-called nonholonomic Noether theorem in terms of our formalism, and we give applications to Riemannian submanifolds, to Lagrangians of mechanical type, and to the determination of quadratic first integrals.

VECTOR FIELDS, VARIATIONAL EQUATIONS AND COMMUTATORS

2012 ◽  
Vol 22 (08) ◽  
pp. 1250190
Author(s):  
WILLI-HANS STEEB ◽  
YORICK HARDY ◽  
IGOR TANSKI
Keyword(s):  
Vector Field ◽  
Differential Equations ◽  
Fixed Points ◽  
Lie Algebra ◽  
Autonomous System ◽  
Vector Fields ◽  
Autonomous Systems ◽  
First Integrals ◽  
Variational Equations ◽  
First Order

We study autonomous systems of first order ordinary differential equations, their corresponding vector fields and the autonomous system corresponding to the vector field of the commutator of two such autonomous systems. These vector fields form a Lie algebra. From the variational equations of these autonomous systems, we form new vector fields consisting of the sum of the two vector fields. We show that these new vector fields also form a Lie algebra. Results about fixed points, first integrals and the divergence of the vector fields are also presented.

scholarly journals Complex Dynamics of Some Hamiltonian Systems: Nonintegrability of Equations of Motion

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Jingjia Qu
Keyword(s):  
Galois Group ◽  
Dynamic Behavior ◽  
Hamiltonian Systems ◽  
Complex Dynamics ◽  
Large Range ◽  
Equations Of Motion ◽  
Differential Galois Group ◽  
Variational Equations ◽  
Particular Solutions ◽  
Double Well Potential

The main purpose of this paper is to study the complexity of some Hamiltonian systems from the view of nonintegrability, including the planar Hamiltonian with Nelson potential, double-well potential, and the perturbed elliptic oscillators Hamiltonian. Some numerical analyses show that the dynamic behavior of these systems is very complex and in fact chaotic in a large range of their parameter. I prove that these Hamiltonian systems are nonintegrable in the sense of Liouville. My proof is based on the analysis of normal variational equations along some particular solutions and the investigation of their differential Galois group.

scholarly journals SYMMETRIES AND FIRST INTEGRALS FOR NON-VARIATIONAL EQUATIONS

2007 ◽  
Vol 04 (07) ◽  
pp. 1217-1230
Author(s):  
DIEGO CATALANO FERRAIOLI ◽  
PAOLA MORANDO
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Vector Fields ◽  
First Integrals ◽  
Partial Differential ◽  
Variational Equations ◽  
First Order ◽  
The Ideal

For a class of exterior ideals, we present a method associating first integrals of the characteristic distributions to symmetries of the ideal. The method is applied, under some assumptions, to the study of first integrals of ordinary differential equations and first order partial differential equations as well as to the determination of first integrals for integrable distributions of vector fields.

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