An object of mass m is propelled vertically upward by a rocket with force F(t). When it is at height (elevation) Y from

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An Object Of Mass M Is Propelled Vertically Upward By A Rocket With Force F T When It Is At Height Elevation Y From 1 (8.72 KiB) Viewed 33 times

An Object Of Mass M Is Propelled Vertically Upward By A Rocket With Force F T When It Is At Height Elevation Y From 2 (3.38 KiB) Viewed 33 times

An Object Of Mass M Is Propelled Vertically Upward By A Rocket With Force F T When It Is At Height Elevation Y From 3 (16.91 KiB) Viewed 33 times

An object of mass m is propelled vertically upward by a rocket with force F(t). When it is at height (elevation) Y from the earth's surface, the gravitational pull F, is given by
F = mg = R R+Y where R is the average radius
Taking the velocity v and the gravitational spring force F, as the state vari- ables (Note: This is the systematic and unified approach where we choose the across-variable v of the A-type element-mass, and the through-variable F, of the T-type element-spring, as the state variables) and F(t) as the input vari- able, develop a state-space model for the mass dynamics.