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This paper is related to the inverse-dynamic modeling of mobile multibody systems articulated with joints and wheels. An easily-implementable algorithm, which is based on Newton-Euler (NE) recursive dynamics, is proposed. From imposed joint and/or actuated-wheel motions, the algorithm performs fast calculations of the control torques, as well as the overall rigid motions involved in locomotion tasks. The engineering applications include tree-like mobile manipulators, satellite-reorientation systems, and modular robots, such as snake-like robots, eel-like robots, and a snakeboard.