Kinematics

Question 1

what does the 1st derivative approximation exclude

Answer 1

the point of interest

Question 2

What does the 2nd derivative approximation exclude

Answer 2

event

Question 3

First order central differences: xi

Answer 3

point about which central differeence is being approximated

Question 4

First order central differences: x(i+1)

Answer 4

the point to the right of xi

Question 5

First order central differences: x(i-1)

Answer 5

the point to the left of xi

Question 6

First order central differences: delta t

Answer 6

time interval between samples

Question 7

First order central differences: O(t)

Answer 7

error associated with the approximation (squared)

Question 8

what is this equation

Answer 8

1st derivative 1st forward difference

Question 9

what is this equation

Answer 9

2nd derivative 1st forward difference

Question 10

what is this equation

Answer 10

1st derivative 1st backward difference

Question 11

what is this equation?

Answer 11

2nd derivative 1st backward difference

Question 12

What is this equation?

Answer 12

1st derivative: second order central diff

Question 13

what is this equation

Answer 13

Second order central difference: 2nd derivative

Question 14

what is this equation

Answer 14

2nd derivative 2nd forward diff

Question 15

what si this equation?

Answer 15

1st derivative 2nd forward difference

Question 16

what is this equation?

Answer 16

2nd derivative 2nd backward difference

Question 17

error reduction in velocity and acceloration?

Answer 17

increase sampling frequency

Question 18

reasons not to use forward and backwards approximations

Answer 18

susceptible to large errors

Question 19

Recommendations for most human movement

Answer 19

-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

Question 20

What is the difference between first and second order differences?

Answer 20

Second order differences span larger periods of time