CODEWITHSUNDEEP
algorithmmathequation
Matt W
Matt W

Reputation: 12423

Solving a ballistic equation through code

This seems like an incredibly simple problem to solve, but everything I've found about it has been too complex for me to understand.

I have this basic ballistic equation:

ballistic trajectory

Given that I know v, g, x and y, how would I go about finding theta? It's very easy to read on paper, but I don't know how this would be done in code.

[EDIT #3:] My try (with input from answers below) is this:

gx = g*x
brackets = gx^2 + 2*y*v^2
sqrroot = sqrt( v^4 - g*brackets )

top1 = v^2 + sqrroot
theta1 = atan( top1 / gx )

top2 = v^2 - sqrroot
theta2 = atan( top2 / gx )

Upvotes: 0

Views: 826

Answers (5)

chux
chux

Reputation: 153498

A c solution

#include<math.h>

void MattW_f(double *theta_p, double *theta_n, double g, double v, double x, double y) {
  double v2 = v*v;
  double gx = g*x;
  // No check against sqrt(negative number)
  double discriminant = sqrt(v2*v2 - g*(gx*x + 2*y*v2));
  if (theta_p) {
    // atan2() returns -pi to +pi, it is a 4 quadrant arctan.
    *theta_p = atan2(v2 + discriminant, gx);  
    }
  if (theta_n) {
    *theta_n = atan2(v2 - discriminant, gx);
    }
  }

Upvotes: 0

Gilbert Le Blanc
Gilbert Le Blanc

Reputation: 51445

More like this.

gx = g*x
brackets = g*x^2 + 2*y*v^2
sqrroot = sqrt( v^4 - g*brackets )
top1 = v^2 + sqrroot
theta1 = atan( top1 / gx )
top2 = v^2 - sqrroot
theta2 = atan( top2 / gx )

You have to account for the plus and the minus in your formula.

You calculate the squares before the multiplication. In some languages, you can calculate g*x^2 by calculating g*x*x.

Upvotes: 1

arshajii
arshajii

Reputation: 129507

You're ignoring a solution - you have

top = v^2 + sqrroot

but you also need to do a recalculation with

top = v^2 - sqrroot

to account for the ± in your equation.

So:

top1 = v^2 + sqrroot
top2 = v^2 - sqrroot

theta1 = atan(top1 / gx)
theta2 = atan(top2 / gx)

(I don't know what equation is in your code, but I'm assuming you meant top)

Upvotes: 1

rajah9
rajah9

Reputation: 12339

In your last line, 

theta = atan( equation / gx )

equation is not set. You probably want to substituted top for equation.

It may also help for you to output each intermediate result (gx, brackets, sqrroot, and top). See if there any unexpected intermediate results.

Upvotes: 0

David
David

Reputation: 1136

If you do not have access to the arctan method, you can use a quasi newton algorithm.

Upvotes: 0

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