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A Study on Constrained Dynamical Systems Using Fundamental Equations of Analytical Dynamics

Emami , Mohsen | 2009

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 39094 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Zohoor, Hassan; Sohrabpour, Saeed
  7. Abstract:
  8. Nonholonomic constraints are a vast portion of constraints that happen in variety of dynamics applications such as robotics and control. In this project we present a new form of D’Alembert’s principle and employ it to generalize classical methods of Analytical Dynamics. It results in a new formulations which can be implemented to solve constrained dynamical systems either holonomic or nonholonomic. These formulations do not have any restrictions on the order of the nonholonomic constraints and can analyze high order nonholonomic constraints (HONCs) as well as first order constraints. In addition using these formulation one can find equations of motion of nonholonomic systems without calculating constraint forces. While most of the methods presented so far employ “Lagrange multipliers” to find equations of motion of nonholonomic systems. Lagrange multipliers are extra variables which bring constraint forces into calculations. On the other hand, when it is desired to calculate some of the constraint forces, implementing the presented method it is only needed to calculate the desired constraint forces instead of calculating all of them. By means of the method introduced in this project we have a powerful formulation for analyzing dynamics of constrained systems. Additionally, using this method in solving constrained dynamical systems will decrease the amount of needed calculation
  9. Keywords:
  10. Dalemert Principle ; Motion Equation ; Analytical Dynamics ; Constrained Dynamics System ; High Order Nonholonomic System

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