Physics in Video Games, Apply Torque to Angular Acceleration

I am working on a top driver game project in 2d. I want to manage all physics myself. Im working with this book: for physics implementation.

From now on, my physics engine can handle force on different axes. But I have some problems to simulate the rotation correctly. I am trying to implement some torque to find angular acceleration. So I applied the inertia tensor matrix:

Matrix3 it;
it.setBlockInertiaTensor(Vector3(2, 1, 1), 400);

void setBlockInertiaTensor(const Vector3 &halfSizes, float mass)
    Vector3 squares = halfSizes.componentProduct(halfSizes);
    setInertiaTensorCoeffs(0.3f*mass*(squares.y + squares.z),
        0.3f*mass*(squares.x + squares.z),
        0.3f*mass*(squares.x + squares.y));


To apply torque, I apply force at a point on the body of my car, and I find torque by the transverse product:

player->addForceAtBodyPoint(Vector3(-2000, 1000, 0), Vector3(0, 100, 0));

void AObject::addForceAtBodyPoint(const Vector3 &force, const Vector3 &point)
    Vector3 pt = getPointInWorldSpace(point);
    addForceAtPoint(force, pt);

void AObject::addForceAtPoint(const Vector3 &force,
    const Vector3 &point)
    // Convert to coordinates relative to center of mass.
    Vector3 pt = point;
    pt -= _position;

    _forceAccumulate += force;
    _torqueAccumulate += pt % force;
    //std::cout << "torque x " << pt.x << " y " << pt.y  <<  " z "<< pt.z <<  std::endl;

Vector3 Vector3::operator%(const Vector3 &vector) const
    return Vector3(y*vector.z - z*vector.y,
        z*vector.x - x*vector.z,
        x*vector.y - y*vector.x);


(Modulo% - cross product)

And finally, I am doing all data integration:

void    Player::integrate(float deltaTime)

    addForce(_velocity * -150.0f);

    // Calculate linear acceleration from force inputs.
    _lastFrameAcceleration = _acceleration;
    _lastFrameAcceleration.addScaledVector(_forceAccumulate, _inverseMass);
    // Calculate angular acceleration from torque inputs.
    Vector3 angularAcceleration = _inverseInertiaTensorWorld.transform(_torqueAccumulate);
    // Update linear velocity from acceleration .
    _velocity.addScaledVector(_lastFrameAcceleration, deltaTime);
    // Update angular velocity from  acceleration .
    _rotation.addScaledVector(angularAcceleration, deltaTime);
    // Impose drag.
    _velocity *= pow(_linearDamping, deltaTime);
    _rotation *= pow(_angularDamping, deltaTime);
    // Update linear position.
    _position.addScaledVector(_velocity, deltaTime);
    _position.z = 0;
    // Update angular position
    _orientation.addScaledVector(_rotation, deltaTime);
    // Normalise the orientation, and update the matrice
    // Clear accumulators.


And orientation doesn't work at all. I am not that good at physics, so I think I misunderstand the physical implementation of torque with tensor of inertia ...


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1 answer

If your game is top-down in 2D, you can only have a rotation in the Z direction. I.E. inside and outside the screen. This way you can simplify your task and avoid 3D tensors. In this case, in your car class, I will have a private variable called rotation. eg.

    double angle;
    double tourque;
    void updateTorque(*some way of passing forces*)
        double total_t = 0;
        for each force
            double t = use cosine and length to point to generate a tourque
            total_t = t + total_t
    void update_angle // place your integration routine here and call once per loop




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