Solving Vertical Body Motion with Quadratic Resistance using Closed-form Solution for Ricatti Differential Equation of Constant Coefficients based on Discriminant Criteria

One of problem in mechanics is vertical body motion in upward and downward direction due to gravitational and resistance forces. In this paper, we are interested to analyse the effect of quadratic resistance force respect to the instantaneouly velocity and position of the body. The equation of the vertical body motion affected by gravitational and quadratic resistance forces derived using the second Newton law generally in the form of Riccati differential equation of constant coefficients. Therefore we need a method for solving the mathematics model. For the purpose we introduce a closed form solution for Riccati differential equation of constant coeficients based on discriminant criteria that can be used to solve the analytic model of vertical body motion by simple manner.