A correct simulation should always conserve the Hamiltonian regardless of whether it’s an open or closed system. The Hamiltonian will be used to derive the impact update equations and can also be plotted with respect to time to examine if the simulation is correct. Calculate the Hamiltonian of the system, which is a conserved value in any dynamic system.The equation is shown below where F is a 6-vector consisting of F x, F y, and zeros: Forces in the x b and y b direction are added here to “shake up” the box. Derive the forced Euler-Lagrange (EL) equations to simulate the trajectory of the jack and the box when it is not actively impacting.m is simply the mass of the object and g is the gravity scalar 9.8 m/s 2. M here is defined as the 6圆 three dimensional inertia matrix of the object (note that only inertia about z is being considered here since the simulation is two dimensional) and V b= where the superscript v represents taking the skew-symmetric form of the vector and G represents the transformation matrix (could be G wb or G wj depending on whether one is determining the KE of the jack or box.). Define the total kinetic energy ( KE) and potential energy ( PE) of the system (jack + box).A diagram of the system can be seen in the image below: The jack and box frames have origins at the center of mass (CoM) of both these objects.
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