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## Homework Statement

For a space-based platform B launching a projectile A what are the resultant inertial velocities equations and where do the launch location and projectile end up a little after launch? The platform is rotating and moving thru space and the launch mechanism imparts a fixed N*sec impulse to the projectile. The projectile is not located at the platform CG and the impulse does not act thru the platform CG.

## Homework Equations

Ignore gravity, drag, and launcher friction

Impulse acts at projectile CG

mB = platform mass (mA for projectile)

PB = platform initial inertial position of CG (PA for projectile)

VB = platform initial inertial velocity of CG (VA for projectile)

wB = platform initial inertial rotation rate about its CG (wA for projectile)

IxxB = platform moment of inertia (IxxA for projectile)

F = applied impulse force to projectile at time zero

dt = time period after launch to calculate the launch and projectile location

R = distance vector from platform CG to launch location (i.e. projectile CG at launch)

## The Attempt at a Solution

These are vectors...

Pre-launch:

VA = VB since they are attached

wA = wB since they are attached

R = PA - PB

After launch:

VB(t) = VB - F / mB this is a constant

PB(t) = PB + VB(t) t

wB(t) = wB - F x R / IxxB this is a constant

VA(t) = VA + F / mA + wB(t) x R this is a constant

PA(t) = PA + VA(t) t

R(t) = R rotated (wB(t) t)

Launch location: PL(t) = PB(t) + R(t)

Projectile location: PA(t)

**4. Should I be including more of the parts shown in**https://www.physicsforums.com/showthread.php?t=77434

aA = aB + wBdot x R + w x (w x R) + 2 w x VRel + aRel