By Ying, Shuh-Jing (Benjamin)

The booklet balances idea and alertness and relates all matters to useful difficulties, real-world events, and up to date advances that have an effect on daily life. this article distinguishes itself with a extra entire advent to fresh advancements in dynamics, new and functional purposes to aid the reader bear in mind key theories and makes use of, and an appreciation that the subject material is riddled with ongoing difficulties that want new solutions.

- facts and knowledge showing during this booklet are for informational reasons in basic terms. AIAA and the writer will not be answerable for any harm or harm because of use or reliance, nor do AIAA and the writer warrant that use or reliance could be unfastened from privately owned rights.

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**Extra resources for Advanced Dynamics**

**Example text**

9. Do the following: (a) Using Green's theorem, prove that -~ (xdy- ydx) = A where A is the area enclosed by the curve c. 10. (a) Show that -~ (xydy- y2dx) = A~ (b) -~ (xyZdy - y3dx) ----Ix ,i c where A is the area bounded by C, (Y, y) is its centroid, and Ix its moment of inertia about x axis. 11. If er, eo, and e0 are the unit vectors in spherical coordinates, show that the unit vectors in Cartesian coordinates can be written as i = (e, sin0 + e0 cos 0)cos 4~ - e0 sin~b j = (er sin 0 + e0cos 0) sin4~ + e~bcos ~b k = e,.

32) 20 ADVANCED DYNAMICS Ht / /// Fig. 6 r ~ ~ v ~ m V Relationship between angular and linear momentums. 3 To illustrate the meaning of Eq. 32), let us consider a block as a particle sliding on a straight rod without friction at a uniform velocity of 30 ft/s, as shown in Fig. 7. The rod is in the x - y plane, which is perpendicular to the gravitational force. The angular velocity of the rod is 50 rad/s. The position of the block is 6 in. away from the rotating axis. Determine the force between the block and the rod if the mass of the block is 1/30 slug.

One is a fixed reference frame; the x axis is oriented along the acceleration. The other is moving with a constant velocity along the negative x direction of the fixed reference frame. However, they coincide at the beginning of observation. (a) Find the velocity and position of the particle as a function of time in both reference frames. (b) Find the work done by the force during a time interval t in both frames. (c) Are the results of (b) different in the two frames? If so, are the laws of mechanics different in the two inertial frames of reference?