On Nonholonomic Parametrization

1970 ◽  
Vol 37 (1) ◽  
pp. 128-132
Author(s):  
B. Vujanovic
Keyword(s):  
Dynamical System ◽  
Differential Equation ◽  
Fixed Point ◽  
Rigid Body ◽  
Force Field ◽  
First Integral ◽  
Central Force Field ◽  
The Stability ◽  
Asymmetric Rigid Body ◽  
System Time

This paper is concerned with the problem of obtaining the differential equation of the trajectory of dynamical system. Time is eliminated by means of some first integral linear with respect to the velocities. As an example, the stability of rotation of a heavy asymmetric rigid body with a fixed point under the action of the Newtonian central force field is considered.

STABILITY OF EULER, LAGRANGE AND KOVALEVSKAYA GYROS IN A NEWTONIAN CENTRAL FORCE FIELD WITH SECOND ORDER TERMS

1996 ◽  
Vol 20 (1) ◽  
pp. 41-53
Author(s):  
Zheng-Ming Ge ◽  
Fu-Neng Ku
Keyword(s):  
Fixed Point ◽  
Force Field ◽  
Direct Method ◽  
High Accuracy ◽  
Second Order ◽  
Central Force ◽  
Central Force Field ◽  
Liapunov Direct Method ◽  
Permanent Rotation ◽  
The Stability

The stability of the permanent rotation of the Euler, Lagrange and Kovalevskaya gyros about a fixed point in the Newtonian central force field is investigated by Liapunov direct method, which improve Leimanis’ and Rumiantsev’s result of stability conditions. For the sake of high accuracy, the first and second order terms of R-1 expressed by potential energy of the Newtonian central force field have been considered, where the R is the distance from the fixed point to the center of attraction.

scholarly journals Existence and Uniqueness for the Controllability of a Dynamical System

2019 ◽  
pp. 168-173
Author(s):  
Eli Innocent Cleopas ◽  
Godspower C. Abanum
Keyword(s):  
Dynamical System ◽  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Integro Differential Equation ◽  
Darbo’S Fixed Point Theorem

In this paper, we consider the existence and uniqueness for the controllability of a dynamical system. Here, measure of non-compactness of set was employed to examine the conditions for darbo’s fixed point theorem which is used to established the existence and uniqueness solution for nonlinear integro-differential equation with implicit derivatives.

Another Theorem for Determining the Definiteness of Sign of Functions and Its Applications to the Stability of Permanent Rotations of a Rigid Body

1984 ◽  
Vol 51 (2) ◽  
pp. 430-434 ◽  
Author(s):  
Z.-M. Ge ◽  
Y.-J. Wu
Keyword(s):  
Fixed Point ◽  
Rigid Body ◽  
The Stability ◽  
Permanent Rotations

A new theorem for determining the definiteness of sign of functions is presented. As the examples illustrate, it is applied to the stability of permanent rotations of a rigid body about a fixed point in five cases.

scholarly journals Positive Almost Periodic Solution on a Nonlinear Differential Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
Ni Hua ◽  
Tian Li-xin ◽  
Liu Xun
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Nonlinear Equation ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Almost Periodic ◽  
Positive Almost Periodic Solution ◽  
The Stability

We study the following nonlinear equationdx(t)/dt=x(t)[a(t)-b(t)xα(t)-f(t,x(t))]+g(t), by using fixed point theorem, the sufficient conditions of the existence of a unique positive almost periodic solution for above system are obtained, by using the theories of stability, the sufficient conditions which guarantee the stability of the unique positive almost periodic solution are derived.

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