NON-LINEAR GENERALIZATION OF THE GAUGE AMBIGUITIES OF THE LAGRANGIAN FORMALISM

1991 ◽  
Vol 06 (05) ◽  
pp. 737-748 ◽  
Author(s):  
JOSÉ F. CARIÑENA ◽  
MANUEL F. RAÑADA
Keyword(s):  
Degrees Of Freedom ◽  
Lagrangian Formalism ◽  
Two Degrees Of Freedom ◽  
Gauge Equivalence ◽  
General Properties ◽  
Non Linear

A generalization of the gauge equivalence of Lagrangians is developed. In this approach the different Lagrangians determine not only the same set of solutions but also the same energies. Some general properties are studied and then the case of velocity-free forces is considered. In particular we show the non-existence for n=2 (two degrees of freedom) of such equivalent Lagrangians and that when n=3 the only forces admitting such equivalent Lagrangians correspond to those deriving from central potentials.

Effects of Suspension Design on the Attitudes of a Car during Braking and Acceleration

1973 ◽  
Vol 187 (1) ◽  
pp. 787-794
Author(s):  
J. R. Ellis
Keyword(s):  
Steady State ◽  
Linear Systems ◽  
Degrees Of Freedom ◽  
Coupled Systems ◽  
Two Degrees Of Freedom ◽  
Simulation Techniques ◽  
Non Linear ◽  
Non Linear Systems ◽  
Effort Distribution

Two degrees of freedom models of a car are employed to demonstrate the effects of the suspension derivative ∂ x/∂ z on the pitch and bounce attitudes during braking or accelerating. The work equation is employed to show that brake effort distribution between the axles has a significant effect on the attitudes when anti-dive suspension characteristics are utilized. The steady-state positions in both pitch and bounce are developed for linear systems of typical suspensions that may be either standard or coupled systems. Non-linear systems are considered using simulation techniques. A description of some simulation circuits is contained in an appendix.

Non-linear vibrations in mechanical systems with one or two degrees of freedom

2018 ◽  
Author(s):  
Д.А. Гришко ◽  
◽  
В.В. Лапшин ◽  
Е.С. Студенников ◽  
А.Н. Тарасенко ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Mechanical Systems ◽  
Two Degrees Of Freedom ◽  
Non Linear ◽  
Linear Vibrations
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