Equation of Motion Written in cartesian coordinates, the equations of motion are mar= Tcos(B +a+ar)-Dcos B-Lsin B may=Lcos B+Tsin(B +a+ar)-Dsin B-w State Space Form The equations of motion can be written in the form of equation(2)by introducing the velocities as variables (T/m)cos(B +a+aT)-(D/m)cosB-(L/m)sin B (L/m)cos B+(T/m)sin(B+a+ar)-(D/m)sin B-(w/m) where, T, a and ar are inputs to the model which will typically be a function of time and perhaps x through the control system. Recall that B= tan(ay/uz), and L is by expressions(3),(4)and D, by expressions (5),(6),and(4) ADDITIONAL READING J. L. Meriam and L.G. Kraige, Engineering Mechanics, DYNAMICS, 5th Edition 3/3, 3/4, 3/5(rectangular coordinates only)Equation of Motion Written in cartesian coordinates, the equations of motion are max = T cos(β + α + αT ) − D cos β − L sin β may = L cos β + T sin(β + α + αT ) − D sin β − W (7) State Space Form The equations of motion can be written in the form of equation (2) by introducing the velocities as variables and taking X =   x y vx vy   , F =   vx vy (T /m) cos(β + α + αT ) − (D/m) cos β − (L/m) sin β (L/m) cos β + (T /m) sin(β + α + αT ) − (D/m) sin β − (W/m)   (8) where, T , α and αT are inputs to the model which will typically be a function of time and perhaps X through the control system. Recall that β = tan−1 (vy/vx), and L is by expressions (3), (4) and D, by expressions (5), (6), and (4). ADDITIONAL READING J.L. Meriam and L.G. Kraige, Engineering Mechanics, DYNAMICS, 5th Edition 3/3, 3/4, 3/5 (rectangular coordinates only) 6