KNES 300 Lecture Notes - Lecture 7: Time Series, Finite Difference
22 Feb 2017
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Why did we use forward difference to calculate a1: differentiation problem and acceleration is a derivative, first frame. Why did we use central difference to calculate a2: middle frame. Why did we use backward difference to calculate a3: last frame. Why did we use numerical integration to calculate position: integration problem. Numerical: calculated from numbers, result is a number, discrete: answer to particular times. Analytical: calculated from equations, result is a symbolic equation, continuous: answer at any time. Advantages: continuous: known values for any time, smoothing: removes noise in original data. Disadvantages: derivatives magnify remaining noise, lower-order functions for derivatives, can"t fit the data too well. What are the advantages of calculating kinematics analytically versus numerically: get equations for kinematics that will tell you the kinematics for any point in time, numerically, you only know the points at specific points in time.
