Kinematics Flashcards
what does the 1st derivative approximation exclude
the point of interest
What does the 2nd derivative approximation exclude
event
First order central differences: xi
point about which central differeence is being approximated
First order central differences: x(i+1)
the point to the right of xi
First order central differences: x(i-1)
the point to the left of xi
First order central differences: delta t
time interval between samples
First order central differences: O(t)
error associated with the approximation (squared)
what is this equation
1st derivative 1st forward difference
what is this equation
2nd derivative 1st forward difference
what is this equation
1st derivative 1st backward difference
what is this equation?
2nd derivative 1st backward difference
What is this equation?
1st derivative: second order central diff
what is this equation
Second order central difference: 2nd derivative
what is this equation
2nd derivative 2nd forward diff
what si this equation?
1st derivative 2nd forward difference
what is this equation?
2nd derivative 2nd backward difference
error reduction in velocity and acceloration?
increase sampling frequency
reasons not to use forward and backwards approximations
susceptible to large errors
Recommendations for most human movement
-2nd order forward and backward approximations in combination with 1st order central difference approximation
-estimate acceleration directly from displacement data rather than velocity data
-collect more data than you need then crop
What is the difference between first and second order differences?
Second order differences span larger periods of time
