Abstract: This paper gives a simple approach to designing a controller that minimizes a userspecified control cost for a mechanical system while ensuring that the control is stable. For a usergiven Lyapunov function, the method ...

Abstract: Lagrangians for classically damped linear multidegreesoffreedom dynamical systems are obtained using simple and elementary methods. Such dynamical systems are very widely used to model and analyze small amplitude vibrations ...

Abstract: This paper presents results related to the stability of gyroscopic systems in the presence of circulatory forces. It is shown that when the potential, gyroscopic, and circulatory matrices commute, the system is unstable. ...

Abstract: This paper develops a general form of Gauss’s Principle of Least Constraint, which deals with the manner in which Nature appears to orchestrate the motion of constrained mechanical systems. The theory of constrained motion ...

Abstract: Zero-mass particles are, as a rule, never used in analytical dynamics, because they lead to singular mass matrices. However, recent advances in the development of the explicit equations of motion of constrained mechanical ...

Abstract: This paper develops an alternative description of the general equation of motion for constrained mechanical systems with singular mass matrices. The formulation gives a new explicit equation of motion for such systems and ...

Abstract: Descriptions of reallife complex multibody mechanical systems are usually uncertain. Two sources of uncertainty are considered in this paper: uncertainties in the knowledge of the physical system and uncertainties in the ...

Abstract: This paper deals with finding Lagrangians for damped, linear multidegreeoffreedom systems. New results for such systems are obtained using extensions of the results for single and two degreeoffreedom systems. The solution ...

Abstract: A simple transformation is used to obtain the first integrals and the solutions of the Duffing–van der Pol type equation under certain conditions. It is shown that the system can be totally integrable and this total ...

Abstract: This paper develops an alternative description of the general equation of motion for constrained mechanical systems with singular mass matrices. The formulation gives a new explicit equation of motion for such systems and ...