scholarly journals Geometric Mechanics, Lagrangian Reduction, and Nonholonomic Systems

2001 ◽  
pp. 221-273 ◽  
Author(s):  
Hernán Cendra ◽  
Jerrold E. Marsden ◽  
Tudor S. Ratiu
Keyword(s):  
Nonholonomic Systems ◽  
Geometric Mechanics ◽  
Lagrangian Reduction

scholarly journals Lagrangian reduction of generalized nonholonomic systems

2008 ◽  
Vol 58 (10) ◽  
pp. 1271-1290 ◽  
Author(s):  
Hernán Cendra ◽  
Sebastián Ferraro ◽  
Sergio Grillo
Keyword(s):  
Nonholonomic Systems ◽  
Lagrangian Reduction

scholarly journals Constant curvature coefficients and exact solutions in fractional gravity and geometric mechanics

Open Physics ◽  
2011 ◽  
Vol 9 (5) ◽  
Author(s):  
Dumitru Baleanu ◽  
Sergiu Vacaru
Keyword(s):  
Fractional Derivative ◽  
Fractional Derivatives ◽  
Geometric Mechanics ◽  
Fractional Dynamics ◽  
Constant Matrix ◽  
Curve Flows ◽  
Physical Interactions ◽  
Nonholonomic Manifolds ◽  
Lagrange Mechanics ◽  
Fractional Gravity

AbstractWe present a study of fractional configurations in gravity theories and Lagrange mechanics. The approach is based on a Caputo fractional derivative which gives zero for actions on constants. We elaborate fractional geometric models of physical interactions and we formulate a method of nonholonomic deformations to other types of fractional derivatives. The main result of this paper consists of a proof that, for corresponding classes of nonholonomic distributions, a large class of physical theories are modelled as nonholonomic manifolds with constant matrix curvature. This allows us to encode the fractional dynamics of interactions and constraints into the geometry of curve flows and solitonic hierarchies.

Adaptive state-feedback stabilization of stochastic nonholonomic systems with an unknown time-varying delay and perturbations

2020 ◽  
pp. 014233122097417
Author(s):  
Qinghui Du
Keyword(s):  
State Feedback ◽  
Nonholonomic Systems ◽  
Feedback Stabilization ◽  
Feedback Controller ◽  
Input State ◽  
Time Varying ◽  
Initial State ◽  
State Feedback Controller ◽  
Time Varying Delay ◽  
Varying Delay

The problem of adaptive state-feedback stabilization of stochastic nonholonomic systems with an unknown time-varying delay and perturbations is studied in this paper. Without imposing any assumptions on the time-varying delay, an adaptive state-feedback controller is skillfully designed by using the input-state scaling technique and an adaptive backstepping control approach. Then, by adopting the switching strategy to eliminate the phenomenon of uncontrollability, the proposed adaptive state-feedback controller can guarantee that the closed-loop system has an almost surely unique solution for any initial state, and the equilibrium of interest is globally asymptotically stable in probability. Finally, the simulation example shows the effectiveness of the proposed scheme.

Lagrange equation of another class of nonholonomic systems

1991 ◽  
Vol 12 (8) ◽  
pp. 727-732
Author(s):  
Gao Pu-yun ◽  
Guo Zhong-heng
Keyword(s):  
Lagrange Equation ◽  
Nonholonomic Systems

Adaptive Feedback Control of Nonholonomic Systems with Uncertainties

2014 ◽  
Vol 971-973 ◽  
pp. 337-340
Author(s):  
Gui Ling Ju ◽  
Wei Hai Sun ◽  
Jian Du ◽  
Yun Chang Hang
Keyword(s):  
Feedback Control ◽  
Nonholonomic Systems ◽  
The State ◽  
Output Measurement ◽  
Adaptive Feedback ◽  
Adaptive Feedback Control ◽  
Strongly Nonlinear ◽  
Output Feedback Controller ◽  
Nonlinear Uncertainties ◽  
Switching Control Strategy

This paper deals with the adaptive feedback control for the nonholonomic systems with strongly nonlinear uncertainties. The state-input scaling technique and back-stepping approach are used to design the output feedback controller. In order to make the state scaling effective, a new switching control strategy based on the output measurement of the first subsystem is employed.

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