Direct method in calculus of variations

The direct method in calculus of variations is a way of finding the best answer out of many possible solutions. It works by finding the answer that has the smallest amount of something, usually called an "energy" or "cost" - it's like finding the shortest path or the most fuel-efficient car. To do this, you first consider all the possible solutions and then compare them to each other. You can then pick the best one by picking the solution that gives you the smallest energy or cost.