Differential Equations
03-27-2017, 11:46 PM
Post: #17
 Thomas Okken Senior Member Posts: 1,120 Joined: Feb 2014
RE: Differential Equations
(03-27-2017 07:27 PM)ttw Wrote:  The first derivative of the distance is the velocity.
The first derivative of the velocity is the acceleration.
The first derivative of the acceleration is the jerk.
The first derivative of the jerk is the snap.
The first derivative of the snap is the crackle.
The first derivative of the crackle is the pop.

For really high impact problems (like the rocket sled experiments) high order expansions seem necessary to get an accurate description.
I got my first exposure to real calculus as a freshman Civil Engineering student. During an early practice session, we were shown the basic of stress analysis, with the example of a uniform, prismatic, horizontal beam, supported at both ends. The prof then started defining the beam's weight as a function of distance along the beam (not weight, of course, but density, but you get the idea). Being a uniform prismatic beam, this function is constant.

Then comes the first integral, which gives you shear stress.
The second gives you torque.
The third gives you bend.
The fourth gives you sag.

Any loads are added to the weight function; the specifics of the supports are expressed as boundary conditions.

The whole thing was more complicated than this, of course. The prof didn't just say "integrate shear stress and poof, you get torque" – he worked it all out on the blackboard with diagrams and infinitisemals. And it was extremely cool to see calculus come to life like that, with an extremely tangible real-world application.
 « Next Oldest | Next Newest »

 Messages In This Thread Differential Equations - bshoring - 03-25-2017, 02:13 AM RE: Differential Equations - ttw - 03-25-2017, 03:29 AM RE: Differential Equations - Han - 03-25-2017, 04:45 AM RE: Differential Equations - peacecalc - 03-25-2017, 02:01 PM RE: Differential Equations - TomC - 03-26-2017, 04:36 PM RE: Differential Equations - bshoring - 03-27-2017, 03:49 AM RE: Differential Equations - Dieter - 03-27-2017, 08:22 AM RE: Differential Equations - Didier Lachieze - 03-27-2017, 08:46 AM RE: Differential Equations - Dieter - 03-27-2017, 10:08 AM RE: Differential Equations - Dieter - 03-27-2017, 08:57 AM RE: Differential Equations - Han - 03-27-2017, 06:46 AM RE: Differential Equations - Ángel Martin - 03-27-2017, 08:47 AM RE: Differential Equations - Dieter - 03-27-2017, 09:58 AM RE: Differential Equations - ttw - 03-27-2017, 07:27 PM RE: Differential Equations - Han - 03-27-2017, 08:55 PM RE: Differential Equations - Thomas Okken - 03-27-2017 11:46 PM RE: Differential Equations - bshoring - 03-27-2017, 11:14 PM

User(s) browsing this thread: 1 Guest(s)