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Unformatted text preview: ME 562 Advanced Dynamics Summer 2010 HOMEWORK # 2 Due: June 14, 2010 Q1. Follow the developments in class notes and derive the Frenet’s formulas (summarized on page 19 of the Chapter 2 powerpoints) for a spatial curve. Recall that these formulas relate the rates of change of the unit vectors associated with the ‘path variable’ description of motion of an object to the properties (radius of curvature and twist) of the space curve. They are also shown here on the right. Q2. Toroidal coordinates ( , , ) are useful for magnetohydrodynamic studies in tokamaks. More specifically, consider a torus with radius of the centerline (a circle) to be r . This centerline is in the (x,y) plane. Now, consider a point P whose position we want to write with respect to the observer located at O. Let P’ be the projection of the position of point P on to the (x,y) plane. The line joining this point P’ with O intersects the centerline of the torus at C. We define the coordinates of the point P by using the radial line OC and the inclined line CP. coordinates of the point P by using the radial line OC and the inclined line CP....
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- Fall '10
- Derivative, OC, Coordinate systems, unit vectors, line CP