Consider a satellite equipped with a solar panel that deploys using a spring mechanism. The panel, whe stowed, lies flat against the satellite's body and is locked in place with a locking pin. The panel is deployed to a $90-$degree position by a spring that pasbes the tip of the panel, causing it to rotate around a hinge. The hinge has a $90-$degree angular design, enabling pivotal movement around a central pin. It is specifically designed to allow a solar panel to rotate to its operational position where it will securely rest against the structure stop on the hinges bracket. The panel locks in place once it reaches a $90-$degree angle relative to the satellite's body. List any assumptions used for esch of the sub$-$problems. Hint: It may be beneficial to

setup arbitrary variables for the pin dimensions ie$.$ radius, pin length, etc...

$1\mathrm{.}1$ Describe the traction boundary conditions on the central pin of the locking pin when the spring is providing force to the pabel but it is not yet released from the locking, pin. In this static analyzis, the focus is force interactions at the pin.

$1\mathrm{.}2$ Now describe the traction boundary conditions on the central pin of the hinge when the panel is loched into the deployed $90-$degree position and the satellite is spinning around the center axis of the cylindrical fuselage with a constant angular velocity.

$1\mathrm{.}3$ The satellite breaks up within the atmosphere and falls back to Earth. Incredibly the fuselage does not barn up and finds itself wasbed up on a beech. This fuselage is half filled with a monopropellant called Advanced Spacecraft Energetic Non$-$Toxic $($ASCENT$)$ propellant which has a density of roughly $1\mathrm{.}46\frac{g}{c}{m}^3.$ Describe

the traction boundary conditions on the fuselage structure as shown in the figure below. The cylindrical fuselage is standing up such that one of the circular ends is perfectly resting on the sand.