Difference of two 2-dimensional matrices

Dear all,

I have the x and y positions of a certain object at 1 second intervals in time. The x positions are stored inside a 1xn matrix, where n is the number of seconds for which the data was obtained. The y positions are also stored inside a 1xn matrix, where n is again the number of seconds for which the object was observed. Now I need to obtain the velocity of the object. I could obtain the x and y velocities separately and store them inside two new matrices by using the diff() function on both x and y position matrices, but I need the velocity of the object as a whole. Can anybody please advise what to do? Thanks.

Answer 1

[Star Strider]

There are actually at least a couple ways to go about this. In either situation, I would use both the hypot and gradient functions.

The first option is to use gradient after the distance calculations:

x = sort(rand(20,1));           % Create Data: ‘X’ Position
y = sort(rand(20,1));           % Create Data: ‘Y’ Position
t = sort(rand(20,1));           % Create Data: ‘Time’ 

xyd = hypot(x,y);               % Pythagorean Theorem Distance Calculation

v = gradient(xyd, t);           % Velocity

The second option is to use gradient first to calculate the individual x and y velocities, then use hypot to calculate the net velocity:

vx = gradient(x, t);            % ‘X’ Velocity
vy = gradient(y, t);            % ‘Y’ Velocity
vn = hypot(vx, vy);             % ‘Net’ Velocity

The code is similar in both situations.

I would experiment with both to determine the most accurate calculation. The choice is yours.

[MeEngr]

Thank you so much!

[Star Strider]

My pleasure!

Answer 2

[dpb]

v=diff(y)./diff(t);

[MeEngr]

Hi dpb, I'm sorry but can you please elaborate? What is diff(y)? Is y the name of the y-position matrix? And t the name of the time array? If yes to both questions, then how do I get the total velocity of the object? As in, I need both x and y velocities as a single number.

[dpb]

Sorry, I misread as distance, time vectors, not x,y. See Star to convert to position first...