Modelling circular motion / tangential acceleration

Question

The following pseudo code works for modelling linear acceleration (applying calculateNextStep and doNextStep for each time tick):

class myObject{

    vector positionVector
    vector velocityVector
    vector accelerationVector
    vector forceVector

    function calculateNextStep(){
        resetForceVector()
        calculateNetForces()
    }

    function doNextStep(){
        accelerationVector = forceVector.getCopy()
        accelerationVector.divideBy(mass)
        velocityVector.add(accelerationVector)
        positionVector.add(velocityVector)
    }
}

My understanding is that for circular motion we need to apply a force orthogonal to the velocity of the object. The size of that force will determine the radius of the circle:

    function calculateNextStep() {
        resetForceVector()
        orthogonalForce = velocityVector.getCopy.getOrthogonalVector()
        orthogonalForce.setLength(sizeOfForce)
    }

When I apply this approach the object doesn't travel in a circular path. Instead it spirals outwards, increasing in velocity.

I assume this is because the tangential force only applies instantaneously ie. as soon as the object moves the tangential force should change accordingly but I don't know how to account for this in my model.

I assume this has been tackled before but can't find anything. Is there a correction term I should be applying? Something to do with limits / integrals?

Answer 1

This question was based on trying to apply linear mechanics to a problem of angular mechanics!

Circular motion only happens if the force is orthogonal to motion and the direction of motion is turning!

I resolved this by adding angular velocity to the model

class myObject{

    vector positionVector
    vector velocityVector
    vector accelerationVector
    vector forceVector
    scalar mass

    scalar torque
    scalar angularAccelleration
    scalar angularVelocity
    scalar orientation
    scalar rotationalInertia

    function calculateNextStep(){
        resetForceVector()
        angularAccelleration = 0
        calculateNetForces()

    }

    function doNextStep(){
        accelerationVector = forceVector.getCopy()
        accelerationVector.divideBy(mass)
        velocityVector.add(accelerationVector)
        positionVector.add(velocityVector)

        angularAcceleration = torque / rotationalInertia
        angularVelocity += angularAccelleration
        orientation += angularVelocity

    }
}