You do not need advanced maths to make good motion, but a few ideas make a big difference.
Interpolation
Almost every animation is a value moving from A to B. Linear interpolation is mechanical; adding an easing curve gives it intention. Ease-out for things arriving, ease-in for things leaving.
Springs
Springs respond to interruption gracefully. If a user changes their mind halfway through, a spring adjusts from its current position instead of restarting.
Noise
Smooth noise adds organic variation to particles, colour and position. It is the basis of the Noise Field study and most of my shader work.
- Use easing for UI transitions
- Use springs for direct manipulation
- Use noise for organic texture