Poincaré-MacMillan Equations of Motion for a Nonlinear Nonholonomic Dynamical System

2012 ◽  
Vol 29 (3) ◽  
pp. 034502
Author(s):  
Amjad Hussain ◽  
Syed Tauseef Mohyud-Din ◽  
Ahmet Yildirim
Keyword(s):  
Dynamical System ◽  
Equations Of Motion ◽  
Nonholonomic Dynamical System

A DYNAMICAL SYSTEM WITH CHAOTIC BEHAVIOR

1989 ◽  
Vol 03 (15) ◽  
pp. 1185-1188 ◽  
Author(s):  
J. SEIMENIS
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Infinite Number ◽  
Chaotic Behavior ◽  
Equations Of Motion ◽  
Hamiltonian Dynamical Systems

We develop a method to find solutions of the equations of motion in Hamiltonian Dynamical Systems. We apply this method to the system [Formula: see text] We study the case a → 0 and we find that in this case the system has an infinite number of period dubling bifurcations.

Weyl–Euler–Lagrange equations on twistor space for tangent structure

2016 ◽  
Vol 13 (07) ◽  
pp. 1650095
Author(s):  
Zeki Kasap
Keyword(s):  
Mathematical Modeling ◽  
Dynamical System ◽  
Classical Mechanic ◽  
Twistor Space ◽  
Equations Of Motion ◽  
Classical Mechanics ◽  
Equation System ◽  
Lagrange Equations ◽  
Four Manifolds ◽  
Riemannian Geometries

Twistor spaces are certain complex three-manifolds, which are associated with special conformal Riemannian geometries on four-manifolds. Also, classical mechanic is one of the major subfields for mechanics of dynamical system. A dynamical system has a state determined by a collection of real numbers, or more generally by a set of points in an appropriate state space for classical mechanic. Euler–Lagrange equations are an efficient use of classical mechanics to solve problems using mathematical modeling. On the other hand, Weyl submitted a metric with a conformal transformation for unified theory of classical mechanic. This paper aims to introduce Euler–Lagrage partial differential equations (mathematical modeling, the equations of motion according to the time) for the movement of objects on twistor space and also to offer a general solution of differential equation system using the Maple software. Additionally, the implicit solution of the equation will be obtained as a result of a special selection of graphics to be drawn.

scholarly journals A dynamical system analysis of f(R,T) gravity

2016 ◽  
Vol 13 (09) ◽  
pp. 1650108 ◽  
Author(s):  
Behrouz Mirza ◽  
Fatemeh Oboudiat
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Equation Of State ◽  
System Analysis ◽  
Equations Of Motion ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Future Singularity ◽  
First Case ◽  
Stress Energy

We investigate equations of motion and future singularities of [Formula: see text] gravity where [Formula: see text] is the Ricci scalar and [Formula: see text] is the trace of stress-energy tensor. Future singularities for two kinds of equation of state (barotropic perfect fluid and generalized form of equation of state) are studied. While no future singularity is found for the first case, some kind of singularity is found to be possible for the second. We also investigate [Formula: see text] gravity by the method of dynamical systems and obtain some fixed points. Finally, the effect of the Noether symmetry on [Formula: see text] is studied and the consistent form of [Formula: see text] function is found using the symmetry and the conserved charge.

Dynamical system generated by the equations of motion of an Oldroyd fluid of order L

1989 ◽  
Vol 47 (2) ◽  
pp. 2399-2403 ◽  
Author(s):  
N. A. Karazeeva ◽  
A. A. Kotsiolis ◽  
A. P. Oskolkov
Keyword(s):  
Dynamical System ◽  
Equations Of Motion ◽  
Oldroyd Fluid

3D DYNAMIC ANALYSIS OF A FLEXIBLE DEPLOYING ARM SUBJECTED TO BASE ANGULAR MOTIONS

2013 ◽  
Vol 13 (02) ◽  
pp. 1350017 ◽  
Author(s):  
P. BAGHERI GHALEH ◽  
S.M. MALAEK
Keyword(s):  
Dynamical System ◽  
Control Systems ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Positioning Accuracy ◽  
Flexible Arm ◽  
Reaction Forces ◽  
Lateral Displacements ◽  
Tip Position ◽  
Flexible Arms

Problems related to the three-dimensional (3D) dynamics of the deploying flexible arms subjected to base angular motions are studied with simulated tip payloads and actual deployment trajectories. To facilitate the solution, an equivalent dynamical system is developed by introducing the inertial reaction forces on the arm, while the equations of motion are derived in the non-Newtonian reference frame attached to the arm. The dynamic behavior of the arm is investigated both by the finite element and assumed Modes methods for the purpose of verification. This study reveals that base angular motions lead to considerable couplings between the two lateral displacements and axial motions. Meanwhile, the induced loadings on the flexible arm due to the base angular motions are obtained, which are useful for the design of more efficient arms. Furthermore, one may use the resulting arm–tip position envelop to predict the antenna positioning accuracy, which paves the way for possible control systems to limit undesirable motions.

ON ANALYTIC AND PERIODIC SOLUTIONS FOR A CLASS OF NONLINEAR OSCILLATORS

1993 ◽  
Vol 03 (02) ◽  
pp. 451-454 ◽  
Author(s):  
JASON A.C. GALLAS
Keyword(s):  
Dynamical System ◽  
Equations Of Motion ◽  
Elliptic Functions ◽  
Nonlinear Oscillators ◽  
Analytic Solutions ◽  
One Dimension ◽  
Trigonometric Functions ◽  
Periodic Functions ◽  
Jacobian Elliptic Functions ◽  
Natural Extensions

We use the equations of motion for a particle moving in one dimension under the action of forces which vary cubically with displacement to discuss differential equations associated with double-periodic Jacobian elliptic functions. We show that analytic solutions for this dynamical system can be given in terms of Jacobian elliptic functions. These periodic functions are natural extensions of the well-known trigonometric functions.

scholarly journals D=10 CHIRAL TENSIONLESS SUPER p-BRANES

1999 ◽  
Vol 14 (20) ◽  
pp. 1335-1347 ◽  
Author(s):  
P. BOZHILOV
Keyword(s):  
Dynamical System ◽  
General Solution ◽  
Equations Of Motion ◽  
Flat Space ◽  
Space Time ◽  
Harmonic Superspace ◽  
Initial Algebra ◽  
Brst Charge ◽  
Arbitrary Gauge

We consider a model for tensionless (null) super-p-branes with N chiral supersymmetries in ten-dimensional flat space–time. After establishing the symmetries of the action, we give the general solution of the classical equations of motion in a particular gauge. In the case of a null superstring (p=1) we find the general solution in an arbitrary gauge. Then, using a harmonic superspace approach, the initial algebra of first- and second-class constraints is converted into an algebra of Lorentz-covariant, BFV-irreducible, first-class constraints only. The corresponding BRST charge is as for a first rank dynamical system.

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