Is Impulse an Approximation in Trajectory Dynamics?

[Shaybay92]

Hi all,

I am reading a book on spacecraft engineering in the section about trajectory dynamics. They define linear and angular momentum as:

$I = \int_{0}^{\tau}{F}dt$ (Linear Momentum)
$L = \int_{0}^{\tau}{T}dt$ (Angular Momentum)

But they (and so many other sources) always mention the fact that it is only used in situations where there is an insignificant amount of movement/rotation change incurred, usually over infinitesimal time periods. Why? Is there some inherent imprecision in these equations? If we know the time function of force or torque, would it not yield a correct value for linear/angular impulse over any period of time we desire?

Very confused. Would really appreciate some clarification here.

Thanks

 

[A.T.]

Is there some inherent imprecision in these equations?

The imprecision is in the values you put in. And for long term predictions those errors can accumulate. Also, in some cases you might have to use relativistic mechanics, of which the classical mechanics is indeed just an approximation.

 

[Shaybay92]

Are you saying that practically speaking we can't know F(t) or T(t)?

Can you elaborate on the relativistic implications?

I am very determined to fully understand this concept. Thank you kindly.

 

[andresB]

The definition of the impulse you wrote is exact, it gives the change on the linear momentum as long as you give the the exact value of the force.

 

[person_random_normal]

I hope you know that impulse acting on a body gives change in momentum of that body, which if we equate to integral F dt or Tdt , and substitute some approximate value of dt (time for which collision lasted) then we can get idea of the value of F (impulsive force) which is huge ,but far lesser than its actual maximum !

As of your question, I didn't understand it !