Impulse is integral of force over time¶

Impulse measures the cumulative effect of a force acting over a finite time interval. Evaluating the time-integral of one Cartesian component of the force yields the corresponding component of the impulse vector.

Conditions:

The force is finite and integrable on the given time interval.

Links:

Wikipedia – Impulse

impulse¶: Projection of impulse vector due to force \(\vec F\).

Symbol:: J
Latex:: \(J\)
Dimension:: momentum

time¶: time.

Symbol:: t
Latex:: \(t\)
Dimension:: time

force¶: Projection of force \(\vec F\) as a function of time.

Symbol:: F(t)
Latex:: \(F{\left(t \right)}\)
Dimension:: force

time_before¶: Initial time of collision.

Symbol:: t_0
Latex:: \(t_{0}\)
Dimension:: time

time_after¶: Final time of collision.

Symbol:: t_1
Latex:: \(t_{1}\)
Dimension:: time

law¶

J = Integral(F(t), (t, t_0, t_1))

Latex:: \[J = \int\limits_{t_{0}}^{t_{1}} F{\left(t \right)}\, dt\]