How do I calculate the acceleration using only 3D distances?

15 vues (au cours des 30 derniers jours)
lil brain
lil brain le 15 Avr 2022
Commenté : Les Beckham le 18 Avr 2022
I have a list of distances in each cell of acc_dist . The first three columns in each cell are xyz coordinates. So column one are all x, column two are all y, and column three are all z. The rows are the coordinate points measured at a speed of 72 Hz.
I am trying to compute the acceleration of these coordinate points by first calculating the 3D euclidean distance between each point and the adjacent point like so:
And then I am trying to use the acceleration formula like so:
acceleration = dv/dt
dv = change in velocity
dt = change in time
How would I go about calculating the acceleration for the entire length of each list?
Thank you!
  4 commentaires
Walter Roberson
Walter Roberson le 15 Avr 2022
Use gradient() twice.
However... acceleration is a signed vector quantity, derived from velocity which is a signed vector quantity. This is a problem for you because sqrt((x2-x1).^2+(y2-y1).^2+(z2-z1).^2) is not signed and not a vector. You are calculating speed, not velocity.
lil brain
lil brain le 15 Avr 2022
Modifié(e) : lil brain le 15 Avr 2022
@Walter Roberson I dont think I follow could you elaborate on that?

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Les Beckham
Les Beckham le 15 Avr 2022
Modifié(e) : Les Beckham le 15 Avr 2022
load acc_dist.mat
xyz = cell_of_double_pre_ballsCopy{1};
dxyz = diff(xyz); % difference between adjacent points in xyz coordinates
v = sqrt(dxyz(:,1).^2 + dxyz(:,2).^2 + dxyz(:,3).^2) * 72;
a = gradient(v, 1/72);
t = 0:1/72:(length(a)-1)/72;
  13 commentaires
Walter Roberson
Walter Roberson le 17 Avr 2022
"Apply this function to every element of this array" is one of the fundamental array operations in theory.
Consider for example,
A = [1 3 5]
A = 1×3
1 3 5
B = A.^2
B = 1×3
1 9 25
From a theoretical perspective, this is not "squaring the vector": from a theoretical perspective, it is "Apply the function x->x^2 to each element of A, returning an array of the results.
This is frequenty called the "map" operation. And having a brief call that says that you are mapping a function over all of the elements of an array, is often significantly clearer than using a for loop.
Les Beckham
Les Beckham le 18 Avr 2022
Point taken. Thanks for clarifying.

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