By Mark D Ardema

ISBN-10: 0306486814

ISBN-13: 9780306486814

ISBN-10: 0306486822

ISBN-13: 9780306486821

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Problem 1/16 1/17. The shape of the stationary cam is that of a limacon, defined by r = b — ccosO, b > c. Determine the magnitude of the total acceleration as a function of 9 if the slotted arm rotates w^ith a constant angular rate co = 0 in the counter clockwise direction. 1/18. A radar used to track rocket launches is capable of measuring r, f, 0, and 9. The radar is in the vertical plane of the rocket's flight path. 0072 rad/s^. What direction is the rocket heading relative to the radar at this time?

1-22. Introduce a frame {i',j', k'} with origin at the body's center of mass that moves in such a way that it's axes always remain parallel to those of the inertial frame (thus this frame is not body fixed). Let the coordinates of mass particle r (with mass m^) be {xr,yr,Zr) and {Cr,ilr,'^r) in the inertial and the other frame, respectively. 58) r where m = 2J"^r- is the mass of the body. Note that, like Eqn. 56), r this equation divides T into a translational and a rotational part. Fig. 1-22 Analytical 22 Dynamics Fig.

V relative to x, y, z be £1 mi ni £2 rn2 ^2 k rnz na Analytical 54 Dynamics Fig. 2-9 Fig. 2-8 (For example, ii is the cosine of the angle between ^ and x). The coordinates of the r^^ particle of the rigid body are then Xr =X + £i(r + hVr + h^r yr = y + mi(r + m^'qr + mzUr Zr —'Z + ni(r + "2'7r + n^Uj- Due to the orthogonality of the direction cosine matrix, the direction cosines are functions of three independent angles, say 9i, 02, 03- Thus the location of all the points of the rigid body are specified by {x, y, 'z, 9i, ^2,^3) relative to the other frame, and therefore the body has 6 DOF.

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