Numerical Modeling Extra Credit Project
Theory
Describing the motion of a particle – its position, velocity and acceleration as a function
of time – can be achieved fairly easily if the system is not too complex.
However, nature
quickly can become very complex, so much that an analytical solution (an equation for
position or velocity as a function of time) can be too mathematically complex to attain.
Numerical modeling techniques can often be used to solve such systems.
Most of these numerical modeling methods involve taking a rather complicated system –
perhaps one in which the acceleration varies with position, speed or time – and breaking
into small intervals (of distance or time) and assuming that the acceleration is constant
over each small interval.
The smaller the interval, the closer the approximation is to
reality.
The Euler Method is a numerical modeling method that breaks a complicated motion into
discrete intervals of time, and assumes that the acceleration is constant over each interval.
The relation between the acceleration and velocities for some small time interval
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 Spring '10
 Lawlor
 mechanics, Numerical Analysis, Acceleration, Velocity, Numerical Modeling

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