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lec13 (1)

# lec13 (1) - Lecture Outline 1 2.003J/1.053J Dynamics and...

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Cite as: Sanjay Sarma, course materials for 2.003J/1.053J Dynamics and Control I, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 1 Lecture Outline 2.003J/1.053J Dynamics and Control I, Spring 2007 Professor Sanjay Sarma 4/2/2007 Lecture 13 Lagrangian Dynamics: Generalized Coordinates and Forces Lecture Outline Solve one problem by Newtonian and Lagrangian Methods. “Lagrangian approach is simple but devoid of insight.” Both methods can be used to derive equations of motion. Figure 1: Wheel on an incline. Figure by MIT OCW. 1. Solve a well-known problem by Newton’s method: Wheel down incline 2. Critique Solution 3. Present Lagrange Equations 4. Solve well-known problem by Lagrange’s Method

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Cite as: Sanjay Sarma, course materials for 2.003J/1.053J Dynamics and Control I, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 2 Example: Wheel Rolling Down Incline Example: Wheel Rolling Down Incline Figure 2: Free body and kinematic diagrams of wheel rolling down incline. The wheel is subject to a normal force, N , a frictional force, F , and a gravitational force, mg . Figure by MIT OCW. What is the acceleration? F = friction 1 degree of freedom, θ . Newton’s Method 3 unknowns: N , F , and θ Equations F = ma F = ma x x y y τ = x-direction: ¨ F + mg sin φ = mr θ y-direction:
Cite as: Sanjay Sarma, course materials for 2.003J/1.053J Dynamics and Control I, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].

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