Consider the gibbs vector defined as where g = (g 1.8283), e = (el, e2. e3) is euler's eigenaxis vector, and θ is the angle associated with euler's eigenaxis rotation. (a) show that the kinematic differential equation for the gibbs vector can be found as gi 82 | =う! g281 83 1+ 8182-83 g183+82][en 83 88283-8i«i 83 8 8382g 18 on or where 0 -83 82 0 81 82 8 0 (b) also show that for infinitesimal rotations, we have

What are the three ways that an object can accelerate

You are driving directly behind a pickup truck, going at the same speed as the truck. a crate falls from the bed of the truck to the road. (a) will your car hit the crate before the crate hits the road if you neither brake nor swerve? (b) during the fall, is the horizontal speed of the crate more than, less than, or the same as that of the truck?

Asquare 1m x 1m plate is shown below. all four of its edges are kept at 0 co. at t=0the temperature distribution is given by: y xtsins n75)=.a) using separation of variables determine the temperature distribution t(x, y,t)along the plate at any time t. b) discretize the heat conduction equation +=22222 txtusing a second-order centered difference scheme for the two second derivatives and a first-order forward euler scheme for the first derivative. using von neumann stability analysis, determine the stability criterion for the proposed discretization scheme in terms of , hand t. solve for the maximum allowable time step tmax