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After achieving the space X missions, the space shuttle carry the crewed capsule back to earth. Well above earth's atmosphere, at height h, its thruster launch the crewed capsule at speed vo with elevation angle a relative to local horizon (refer to Figure 1). Derive the equation of motion of the crewed capsule using (a) Newtonian mechanics, (b) Lagrange's methods, and (c) Hamiltonian method.

After achieving the space X missions, the space shuttle carry the crewed capsule back to earth. Well above earth's atmosphere, at height h, its thruster launch the crewed capsule at speed vo with elevation angle a relative to local horizon (refer to Figure 1). Derive the equation of motion of the crewed capsule using (a) Newtonian mechanics, (b) Lagrange's methods, and (c) Hamiltonian method.

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earth surface Figure 1. After achieving the space X missions, the space shuttle carry the crewed capsule back to earth. Well above earth's atmosphere, at height h, its thruster launch the crewed capsule at speed vo with elevation angle a relative to local horizon (refer to Figure 1). Derive the equation of motion of the crewed capsule using (a) Newtonian mechanics, (b) Lagrange's methods, and (c) Hamiltonian method. Note: You may use plane polar coordinates coincide with Cartesian's xz plane.
Transcribed Image Text:earth surface Figure 1. After achieving the space X missions, the space shuttle carry the crewed capsule back to earth. Well above earth's atmosphere, at height h, its thruster launch the crewed capsule at speed vo with elevation angle a relative to local horizon (refer to Figure 1). Derive the equation of motion of the crewed capsule using (a) Newtonian mechanics, (b) Lagrange's methods, and (c) Hamiltonian method. Note: You may use plane polar coordinates coincide with Cartesian's xz plane.
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