Caco-Physics
This project is based on the idea that a new collision detection and response system can be part of the cacophonia project and can also stand alone as an external library for those using the same programming tools as the cacophonia project. hense the title for this project can simple be put as "The design, development and integration of a collision detection and response system "Caco-physics", to a music strategy Game "Cacophonia"." Collision detection and response systems are used in many applications from simple physics simulation to advanced gaming and natural world simulation. this projects uses Physics principles to simulate collision detection and the response system.

Time Integration of Motion in Caco-Physics

TimeIntegration

Time integration of motion in physics simulation has to be accurate and stable. The time integration algorithms are algorithms that are required to simulate and integrate the newton's laws of motion of interacting bodies and follow the laws of motion. Note that there are relationships between the position, velocity and acceleration of a body, this algorithm is where the relationship between these dynamics of a body is simulated over time.

There are always numerical errors in integration methods/algorithms, the larger the error the less the precision of the algorithm the smaller the error the more precision of the algorithm. These errors are called truncation error or round-off errors.

There are several integration algorithms that one had to explore before picking and implementing a stable and efficient form of integration. The integration algorithms included in this project are Verlet integration algorithm, simplistic Euler integration, Runge- Kutta methods, Newmark Scheme, forward Euler integration and backward Euler integration.

The position update is done in this algorithm taking into account the velocity and acceleration of a body and the velocity will depend on the acceleration and the acceleration will depend on the mass of the body and the forces acting upon the body. The time integration algorithm in Caco-Physics are carefully selected for different applications of simulation. 

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