This assignment is intended to have you explore Matlab beyond what you will ever need in your lifetime!. Actually, it is to have you take things to the next level. Matlab has a built in symbolic manipulator. This means that you can formulate equations of motion with reaction forces in a Newton-Euler formulation and rearrange symbolically in Matlab to get the equations of motions. You are to examine a double pendulum with link 1 (to ground) being 30 cm long and link 2 being 20 cm. Assume that the links are 2.5 cm wide and 1 cm think. Pivots are placed on the ends (think theoretically). While are solve the double pendulum, first you want solve a single pendulum. The to initial conditions for the two pendula are theta_1 = theta _2 =90 degree. Plot the tip positions an -y plot for 3 minutes every second. Formulate the equations of motion in an x-y coordinate system with theta_1 = theta_2 = 0 degree when the pendula are hanging vertically down. You are to submit this as an email with your handwritten derivation of the equations as a pdf (imbed the plots at the end) and also as a two separate Matlab files. You are not to copy anyone's program off of the internet, your program should be unique from your classmates as well as everyone else's in the world (or universe if they are using Matlab somewhere else)