1. The problem statement, all variables and given/known data The following series of differential equations represents a projectile's path when solved (g=9.81): Modify this series of differential equations to account for an additional force F with vector components a and b acting on the projectile. Here is a sample plot of this system: 2. Relevant equations See above. 3. The attempt at a solution Knowing that gravity is a force with a positive i-component and negative j-component, I attempted to apply the same logic to F. This resulted in: vdot = -g*sin(theta) + a*cos(theta) + b*sin(theta) and thetadot = -g/v*cos(theta) + a/v*sin(theta) + b/v*cos(theta) However, that solution didn't appear to be correct, as when I plotted this out with F with a positive i-component and a negative j-component, I got this plot: From intuition, the positive i-component should have caused the projectile path to move to the right more (hard to describe in words, but I hope you get what I mean), but instead, with my system (somehow), the projectile somehow happens to move to the left and go to the negative x-axis. Because my attempt to apply how gravity was represented in this system to how an arbitrary force would be represented, well, failed, I am currently stuck. As this is my first post, I'm not sure whether it belongs in the introductory or advanced section (as it involves differential equations, but is a simple system). Sorry in advance if it's wrong.