Hamiltonian mechanics and nonlinear dynamics of a body subject to time-varying gyroscopic and potential forces

2012 ◽  
Author(s):  
Scott David Kelly ◽  
Joris Vankerschaver
Keyword(s):  
Nonlinear Dynamics ◽  
Hamiltonian Mechanics ◽  
Time Varying ◽  
Body Subject ◽  
Potential Forces

scholarly journals Nonlinear Dynamics of a Spur Gear Pair with Time-Varying Stiffness and Backlash

2004 ◽  
Vol 23 (3) ◽  
pp. 179-187 ◽  
Author(s):  
Shen Yongjun ◽  
Yang Shaopu ◽  
Pan Cunzhi ◽  
Liu Xiandong
Keyword(s):  
Nonlinear Dynamics ◽  
Spur Gear ◽  
Time Varying ◽  
Gear Pair

Adaptive second-order consensus of multi-agent systems with heterogeneous nonlinear dynamics and time-varying delays

2013 ◽  
Vol 118 ◽  
pp. 289-300 ◽  
Author(s):  
Bo Liu ◽  
Xiaoling Wang ◽  
Housheng Su ◽  
Yanping Gao ◽  
Li Wang
Keyword(s):  
Nonlinear Dynamics ◽  
Second Order ◽  
Time Varying ◽  
Multi Agent Systems ◽  
Agent Systems ◽  
Multi Agent

Analysis of Nonlinear Dynamics for a Rotor-Active Magnetic Bearing System With Time-Varying Stiffness: Part I — Formulation and Local Bifurcations

2003 ◽  
Author(s):  
Wei Zhang ◽  
Jean W. Zu
Keyword(s):  
Nonlinear Dynamics ◽  
Steady State ◽  
Transient State ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Time Varying ◽  
Quasiperiodic Solutions ◽  
Local Bifurcations ◽  
Averaged Equations ◽  
Amb System

In this two-part paper, we investigate nonlinear dynamics in the rotor-active magnetic bearings (AMB) system with 8-pole legs and the time-varying stiffness. The model of parametrically excited two-degree-of-freedom nonlinear system with the quadratic and cubic nonlinearities is established to explore the periodic and quasiperiodic motions as well as the bifurcations and chaotic dynamics of the system. The method of multiple scales is used to obtain the averaged equations in the case of primary parameter resonance and 1/2 subharmonic resonance. In Part I of the companion paper, numerical approach is applied to the averaged equations to find the periodic, quasiperiodic solutions and local bifurcations. It is found that there exist 2-period, 3-period, 4-period, 5-period, multi-period and quasiperiodic solutions in the rotor-AMB system with 8-pole legs and the time-varying stiffness. The catastrophic phenomena for the amplitude of nonlinear oscillations are first observed in the rotor-AMB system with 8-pole legs and the time-varying stiffness. The procedures of motion from the transient state chaotic motion to the steady state periodic and quasiperiodic motions are also found. The results obtained here show that there exists the ability of autocontrolling transient state chaos to the steady state periodic and quasiperiodic motions in the rotor-AMB system with 8-pole legs and the time-varying stiffness.

Analytical Solutions for a Spinning Rigid Body Subject to Time-Varying Body-Fixed Torques, Part I: Constant Axial Torque

1993 ◽  
Vol 60 (4) ◽  
pp. 970-975 ◽  
Author(s):  
J. M. Longuski ◽  
P. Tsiotras
Keyword(s):  
Rigid Body ◽  
Equations Of Motion ◽  
Analytic Solutions ◽  
Axisymmetric Body ◽  
Attitude Motion ◽  
Time Varying ◽  
Torque Vector ◽  
Constant Torque ◽  
Symmetric Rigid Body ◽  
Body Subject

Analytic solutions are derived for the general attitude motion of a near-symmetric rigid body subject to time-varying torques in terms of certain integrals. A methodology is presented for evaluating these integrals in closed form. We consider the case of constant torque about the spin axis and of transverse torques expressed in terms of polynomial functions of time. For an axisymmetric body with constant axial torque, the resulting solutions of Euler’s equations of motion are exact. The analytic solutions for the Eulerian angles are approximate owing to a small angle assumption, but these apply to a wide variety of practical problems. The case when all three components of the external torque vector vary simultaneously with time is much more difficult and is treated in Part II.

Stability Analysis of a Linearized MEMS

2004 ◽  
Author(s):  
A. Khazaei ◽  
M. Rastgaar Aagaah ◽  
M. Mahinfalah ◽  
N. Mahmoudian ◽  
G. Nakhaie Jazar
Keyword(s):  
Nonlinear Dynamics ◽  
Stability Analysis ◽  
Frequency Response ◽  
Dynamic Behavior ◽  
Stability Theory ◽  
Perturbation Methods ◽  
Time Varying ◽  
Design And Optimization ◽  
System Parameters ◽  
The Stability

This paper presents the stability theory and dynamic behavior of a micro-mechanical parametric-effect resonator. The device is a MEMS time-varying capacitor. The nonlinear dynamics of the MEMS are investigated analytically, and numerically. Applying perturbation methods, and deriving an analytical equation to describe the frequency response of the system enables the designer to study the effect of changes in the system parameters that can be used for design and optimization of the system.

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