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Using the main author's researches on the energies of acceleration and higher order equations of motion, this paper is devoted to new formulations in analytical dynamics of mechanical multibody systems (MBS). Integral parts of these systems are the mechanical robot structures, serial, parallel or mobile on which an application will be presented in order to highlight the importance of the differential motion equations in dynamics behavior. When the components of multibody mechanical systems or in its entirety presents rapid movements or is in transitory motion, are developed higher order variations in respect to time of linear and angular accelerations. According to research of the main author, they are integrated into higher order energies and these in differential equations of motion in higher order, which will lead to variations in time of generalized forces which dominate these types of mechanical systems. The establishing of these differential equations of motion, it is based on a generalization of a principle of analytical differential mechanics, known as the D`Alembert – Lagrange Principle.

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In this paper the dynamics equations for a mobile robot, named PatrolBot, will be developed, using new concepts in advanced mechanics, based on important scientific researches of the main author, concerning the kinetic energy. In keeping the fact that the mathematical models of the mobile platforms are different besides the other robots types, due to nonholonomic constraints, these dynamic control functions, will be computed, according to these restrictions for robot motion.

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