A function to calculate velocity in pandas dataframe

Question

I was wondering if there was some function/library that can calculate velocity in a pandas dataframe. I have the following dataframe:

Time    bar_head_x  bar_head_y  bar_head_z
0.00    -203.3502   1554.3486   1102.8210
0.01    -203.4280   1554.3492   1103.0592
0.02    -203.4954   1554.3234   1103.2794   
0.03    -203.5022   1554.2974   1103.4522

From this I want to calculate speed, velocity and acceleration. Speed and acceleration are easy: I used np.linalg.norm to calculate the speed, like so:

speed['head'] = np.linalg.norm(speed[['bar_head_x','bar_head_y','bar_head_z']].values,axis=1)

and .diff() to calculate acceleration from speed, like so:

acc['acc_head'] = (speed['head'].diff()) / ((speed['Time'].diff()))

But how would I go about calculating velocity in such a simple way? Is there such a way - a function to help do this?

Thanks!

@AnnZen more like a timeseries of velocity, so at each index (0-3 above) I would like to have a velocity vector — Oam, Jun 18 '20 at 13:06
@SurajSubramanian Yes, for acceleration I create a new df named acc, but yes. — Oam, Jun 18 '20 at 13:24

warped · Accepted Answer · 2020-06-18T14:09:35.553

df.diff() gives you the next minus the current row.

Since your bar_head... columns indicate position, the differences generated by df.diff can be intepreted as the vectors pointing from current to next positions. np.linalg.norm of these vectors gives you the length of the vectors, i.e. distance travelled per interval. Division by the time interval gives velocity.

diff = df.diff()

coords = [c for c in df.columns if not 'Time' in c]
np.linalg.norm(diff[coords], axis=1)/diff['Time']


0          NaN
1    25.058420
2    23.172492
3    17.487733

edit:

explananation for the 2D case

suppose we have the following dataframe:

df = pd.DataFrame({'time':[0,1], 'x':[1,2], 'y':[1,2]})

    time    x   y
0   0       1   1
1   1       2   2

at time=0 we are at position [1,1] at time=1 we have moved to position [2,2]

so, we have traveled 1 in direction x and 1 in direction y. Our total distance travelled is sqrt(1^2 + 1^2) = sqrt(2)

using df.diff(), we get

    time    x   y
0   NaN     NaN NaN
1   1.0     1.0 1.0

Here, we interpret the 1.0, 1.0 in row 1 as the vector that points from our position at time t=0 to our position at time t=1.

The length of that vector can be computed by its norm, and likewise evaluates to the square root of 2.

So, we can use np.linalg.norm to calculate the distance travelled per time interval.

The velocity is simply (distance travelled)/(length of time interval)

with the dataframe you provided, this outputs four values, corresponding to the velocity at each timepoint. I have edited the output into the answer — warped, Jun 18 '20 at 13:45
So at each time point, velocity is a scalar associated with the position vectors at that index? If so, why? (Sorry, it's been a while since i've studied these so can't remember it well) — Oam, Jun 18 '20 at 13:53

score 1 · Answer 2 · answered Jun 18 '20 at 13:31

If you are looking for velocity as a vector, you can use almost exactly the same code you used to calculate acceleration, except run it over bar_head_x, bar_head_y, and bar_head_z to get the velocity_head_x and so on, for each component of the velocity vector.

A function to calculate velocity in pandas dataframe

2 Answers2

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