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Hamilton’s principle states that among all curves between two end points, the path actually followed by a physical system will always be th one that gives an stationary value (minimum, maximum or a saddle points) to the Hamilton’ s action (an integral over time of the difference between the kinetic and the potential energy, taken between the initial time and the final time of the development of the system). It is common to use a mathematical tool called Calculus of Variations to study the Hamilt on’s principle. The Calculus of Variations deals with functionals (functions of functions ) and is a more general and more complex version of the usual calculus that we learn in univer s ty. In this paper we present an alternative, and simpler, approach to the study of the Hamil ton’s principle. We study the nature of the action’s stationary space-time trajectory of th ree physical systems: free-particle, vertical launch and harmonic oscillator, using as virtual m otion a linear combination of the physical solution of this three systems. We find evidences th at the physical solution of the free-particle problem leads to a minimum on its action. The s ame results occours on the vertical launch problem. The physical solution of the harmo nic oscillator leads to a minimum or a saddle point on its action deppending on the time inte rval of the development of the system.

Uso da combinação linear de soluções físicas no estudo da natureza do ponto estacionário da ação