position += velocity · dt; velocity += acceleration · dt.

v − 2·(v · n)·n, with n the wall’s unit normal.

The angle of the point (x, y), from −π to π.

Leaves the loop it is in, at once.

½·|v|² + g·y should stay nearly constant without friction: a test of a simulation.

Ball in a spinning ring · Python

Flashcards for Python lesson 7: Stepping through time

Read the front, say the back to yourself, then open the card.

Euler step

position += velocity · dt; velocity += acceleration · dt.
Reflection

v − 2·(v · n)·n, with n the wall’s unit normal.
np.arctan2(y, x)

The angle of the point (x, y), from −π to π.
break

Leaves the loop it is in, at once.
Energy check

½·|v|² + g·y should stay nearly constant without friction: a test of a simulation.