By Mark D Ardema

ISBN-10: 0306486814

ISBN-13: 9780306486814

ISBN-10: 0306486822

ISBN-13: 9780306486821

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**Extra info for Analytical dynamics : theory and applications**

**Example text**

6 m—*j Problem 1/44 1/45. The identical links are released simultaneously from rest at ^ = 30° and rotate in the vertical plane. Find the speed of each 2 lb mass when Q = 90°. The spring is unstretched when Q = 90°. Ignore the mass of the links and model the masses as particles. Analytical 38 Dynamics Problem 1/45 1/46. The device shown is released from rest with 0 = 180° and moves in the vertical plane. The spring has stiffness 900 N/m and is just touching the underside of the collar when 9 = 180°.

Same as Problem 1/31, except that the rod is slowing down at the rate of 2 mm/s^. Analytical 36 Dynamics 1/34. Find the velocity and acceleration of point E for the situation in Problem 1/31. 1/35. Prove Eqn. 56). 1/36. Prove Eqn. 57). 1/37. Prove Koenig's theorem, Eqn. 58). 1/38. Show that Eqn. 58) reduces to Eqn. 57) for the case of 2-D motion. 1/39. Prove Eqn. 59). 1/40. A 50 kg cart slides down an incline from ^ to B as shown. What is the speed of the cart at the bottom at B if it starts at the top at A with a speed of 4 m/s?

5 If these conditions are not met, then the equation contains products as well as moments of inertia. See Ardema, Newton-Euler Dynamics, for a complete discussion of Eulerian dynamics of a rigid body. Review of Newtonian Dynamics 29 PROBLEMS 1/1. A point moves at a constant speed of 5 ft/s along a path given by y = 10e~^^, where x and y are in ft. Find the acceleration of the point when a; = 2 ft. 1/2. A point moves at constant speed v along a curve defined by r = A6, where ^4 is a constant. Find the normal and tangential components of acceleration.

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