There are various integration methods that can be used for games. I am trying to write a simple physics engine deciding between semi-implicit Eular and Verlet variants.

What I don't understand is where most information says that they work well for constant acceleration. Say more than one force acts on a body, and acceleration is calculated using force/mass. Velocity and position are derived from this. This means that the acceleration is not constant surely?

Am I incorrect in my understanding that applying a force in one step, and a different force at another step, is variable acceleration? Is it simply that the error amount is small enough to be ignored. So semi-implicit eular, with fixed time-step but variable acceleration, for example, will be a good approximation?

I'm very confused, I've read so many different things. I'd appreciate any insights. Thanks!

There are various integration methods that can be used for games. I am trying to write a simple physics engine deciding between semi-implicit Euler and Verlet variants.

What I don't understand is where most information says that they work well for constant acceleration. Say more than one force acts on a body, and acceleration is calculated using force/mass. Velocity and position are derived from this. This means that the acceleration is not constant surely?

Am I incorrect in my understanding that applying a force in one step, and a different force at another step, is variable acceleration? Is it simply that the error amount is small enough to be ignored. So semi-implicit Euler, with fixed time-step but variable acceleration, for example, will be a good approximation?

I'm very confused, I've read so many different things. I'd appreciate any insights. Thanks!