Setting: Biomechanics – Gait analysis: components of ground reaction force. In a GRK diagram (with time on the x-axis and GRK on the y-axis), the area under the curve is equal to the momentum. Now my question is: is that momentum equal to the linear moment/amount of motion or not?
Answer
In mechanics, the principle of force and momentum applies:
Impulse at moment t1 + time integral of acting forces = momentum at instant t2
This vector equation indicates that the time integral of acting forces (ie the force pulse) is responsible for a difference between two impulses. Momentum is the product of velocity and mass, and is sometimes referred to as ‘linear moment’ or ‘amount of motion’.
From a theoretical point of view, one should use a vector equation because one will always take into account the direction in which the velocities and forces occur.
In order to use the equation in practice, they are normally split into three directions, for example x- and y-direction (on the ground plane) and the z-direction (perpendicular to the ground plane). The 3 resulting equations look like this:
Impulse at moment t1 in x-direction + time integral of all acting forces in x-direction = momentum at instant t2 in x direction.
Impulse at moment t1 in y-direction + time integral of all acting forces in y-direction = momentum at instant t2 in y direction.
Impulse at moment t1 in z-direction + time integral of all forces acting in z-direction = momentum at instant t2 in z direction.
The acting forces involved are the ground reaction forces in the left and right leg, and the person’s own weight. The latter will therefore only be taken into account in the third equation (in the z-direction).
The time integrals appearing in these equations correspond to the areas under the curves representing the acting forces as a function of time. The acting (ground reaction forces) can be measured with a force plate.
Regards.
Answered by
dr. ir. Tom Claessens
– theoretical mechanics – applied energy theory – applied fluid dynamics
http://www.ugent.be
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