Differential equations of motion in matrix form of multibody systems driven by electric motors


  • Nguyen Quang Hoang Hanoi University of Science and Technology,
  • Vu Duc Vuong Thai Nguyen University of Technology




multibody system, electromechanical system, equations of motion, dynamic models, underactuated system


This paper presents the dynamic model of multibody systems driven by electric motors, the so-called electromechanical systems. The mechanical systems considered in this study include an open loop and/or a closed loop, a full-actuated and an under-actuated one. The dynamic model of this electromechanical systems is established in matrix form by applying the Lagrangian equation with and without multipliers and substructure method. With this approach it is easy to obtain the differential equation of motion of the electro-mechanical systems based on the corresponding differential equations of the purely available mechanical system. These obtained equations describe the electromechanical systems in engineering better in case the systems are purely described by mechanical equations. The differential equations of serial and parallel manipulators, slider-crank mechanism, and overhead crane driven by electric motors are established as illustrated examples. In addition, a simplified dynamic model obtained by neglecting of current variation is also validated by numerical simulations. 


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Author Biographies

Nguyen Quang Hoang, Hanoi University of Science and Technology,

Corresponding Author:
Email: hoang.nguyenquang@hust.edu.vn

Vu Duc Vuong, Thai Nguyen University of Technology

Thai Nguyen University of Technology,


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How to Cite

Hoang, N. Q., & Vuong, V. D. (2019). Differential equations of motion in matrix form of multibody systems driven by electric motors. Vietnam Journal of Mechanics, 41(4), 301–317. https://doi.org/10.15625/0866-7136/13356



Research Paper