- First solve the differential equation of the projectile without worrying about x-axis crossing or how to manipulate the initial angle.
- Next use an events function to identify the x-axis crossing. Here is an example that may be helpful.
- Once you get this to work implement the shooting method. These are a few more lines of code, and this is where you (MATLAB) would do the iterations you are referring to in your question.
Finding the initial conditions which give a specified event using ode45
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I'm using ode45 to solve a system of ODEs which describe the movement of a projectile. I now want to find the initial angle which will result in the projectile crossing the x-axis at a specified point x. Is this possible? I was thinking of some sort of iteration method which tests out different angles until it finds one that works, but I need the angle to 8 significant figures, so I feel as if this would result in a lot of iterations.
Mischa Kim on 11 Jan 2021
as Walter pointed out this is a BVP. However, you can and I personally would use ode45 and the so-called shooting method to solve this problem. I recommend taking a step-by-step approach:
Feel free to share your code if you have more questions.