Analytical dynamics : theory and applications by Mark D Ardema

By Mark D Ardema

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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. Fig. 1/2 Fig. 1/3 Problem 1/2 Problem 1/3 1/3. A point travels along a parabola y = kx"^, k a constant, such that the horizontal component of velocity, x, remains a constant. Determine the acceleration of the point as a function of position. 1/4. Grain is being discharged from a nozzle into a vertical shute with an initial horizontal velocity V_Q .

1/54. A 1/2 lb collar slides without friction on a horizontal rod which rotates about a vertical shaft. 5 lb/ft and unstretched length 9 in. As the rod is rotating at angular speed 12 rad/s the cord is cut, releasing the collar to slide along the rod. The spring is attached to the collar and the rod. Find the angular speed of the rod and the radial and transverse components of the velocity of the collar as the rod passes postion B. Also find the maximum distance from the vertical shaft that the collar will reach.

The Analytical 24 Dynamics only force doing work is weight, mg, and this force is conservative; therefore energy is conserved and Eqn. 47) applies: E = T + V = -m V —mgi cos 6 = constant E = 2-mfee + mgisinee =0 Clearly, method (a) requires the most work and (c) the least. Note that method (c) does not give force T, which may be of interest, and gives a once integrated form of the equation of motion. Robot Link. A rigid body moves in the (a;, y) plane such that one of its points, say B, remains fixed in an inertial frame.

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