A. Frank D'Souza's Advance Dynamics: Modeling and Analysis PDF

By A. Frank D'Souza

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Since m 1 m 2 , m 1 + m 2 ~ m 2 and the equivalent mass of the satellite becomes m 1 m 2 /(m 1 + m 2 ) ~ m 1 , which is its actual mass. Eliminating va for the circular orbit, we obtain + ,+ mz)J'/2 71 to a malfunction of the control, the satellite is not projected horizontally but at an angle a: to the horizontal and, as a result, is projected into an elliptic orbit. Find the perigee and apogee of the orbit. ) First, we consider the circular orbit for which Case 4: e = 0, E = -[G(m 1 m 2 )]2/2h 2 • The orbit is a circle which is a special case of the elliptic orbit.

An approximate answer can be obtained by neglecting drag and it can serve as a guideline for more accurate formulation of the subatmospheric motion. Choosing as shown in Fig. 77) and since at point A of the elliptic orbit = 180°, we get e e. 23 = r;v; for the elliptic orbit. Solving fore, we obtain Orbit of a satellite. e by the spacecraft depends only upon r0 and of IX. 77). 77) we get e. 92) h2 v;r. 92) yields r0 - :. / R for point B of splashdown in (3. v. 24 Splashdown of satellite. 91), we obtain - \ '-..

Contains the components of the vector ifo, whereas the matrix {co}. includes the components of the angular velocity vector It may be noted that both ilo and are independent of the orientation of the xyz coordinate frame having its origin at 0. However, the elements of the matrices {H}. and {co}. depend on the orientation of the coordinate system. If a different coordinate frame Ox'y'z' is used, the vectors H. and will remain unchanged but the column matrices {H'}. and {co'}. will have different elements.

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Advance Dynamics: Modeling and Analysis by A. Frank D'Souza

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