Relative Body Angles of a Human Moving Through Space

[LRino]

Homework Statement

Say a human is moving through space with constant acceleration due to gravity. There are no external forces/torques on the body other than the force of gravity. The person applies an internal torque at some joint, let's say the knees, so that they bend. Assume the rest of the body is rigid. I believe angular momentum is conserved here about the center of mass of the entire body at all times. The resulting motion I care about is the relative knee angle between the upper and lower legs. Would the resulting knee response as a function of time depend on the direction of gravity (i.e. facing the direction of fall vs. facing away from it)?

Homework Equations

Conservation of Angular Momentum
Newton's Third Law

The Attempt at a Solution

I'm trying to formulate equations of motion for a high jumper in midair, and I'm wondering if I could split the problem up by tracking the center of mass of the entire body using simple projectile motion equations and ignoring gravity to solve the relative body angles part. The center of mass and relative body angles would be solved independently as a function of time and then combined later using the definition of center of mass so that the position of the jumper's body parts could be found as a function of time.

 

[mfb]

I believe angular momentum is conserved here about the center of mass of the entire body at all times.

Right.

Gravitation accelerates all body parts in the same way*, it is not relevant for the orientation.
*assuming the human is small compared to the diameter of earth. Certainly a good assumption.

Note that you can change your orientation in space even without external torque and without total angular momentum. Cats are very good at that.

 

[LRino]

Thanks!