Decomposition

Decomposing a problem into parts, each amenable to solution using the S.I.M. approach.

Typical Decompositions

ByTimeorPosition"> By Time or Position

A single body may undergo different interactions during different times or at different positions.  For example, a car may travel at uniform velocity, then the driver may apply the brakes causing deceleration, then the car may collide with something, then come to a stop because the brakes are still applied.  This example requires decomposition into four separate regions.  There are three boundaries between the regions, and for each the position and velocity of the car are the same on each side of the boundary (but may change within each region due to interactions specific to that region).  Since the position and velocity are equal across the boundary, the potential and kinetic energy of the body will be the same across the boundary, suggesting that energy models may well apply to an object moving from a smooth surface on to one with ice, for example.

MultipleSystems"> Multiple Systems

If there are two bodies present it may be preferable to treat them separately, rather than one system.  An example is a faster car that is overtaking a slower one.  Until they collide, they will have different positions vs. time.