TL;DR Summary: Why are the paths of our cosmic explorations, pretty?
OK, so I ask a lot of stupid questions. Here's another.
Why is this picture, below, pretty?
(They are the paths of all our cosmic explorations.)
Now, I get the sine, cosine, circles, gravitational attraction, escape...
OK, be that way ;-) (joking here)
How did they stumble upon this operation?
Did they just try everything under the sun? Why not the cosine of the angle between the vectors.
So, yes, it is useful. But how did they know in advance (when constructing this operation) that it would be useful?
OK, that was good. That was funny. Put a smile on my face.
But could you elaborate?
In my senses, I see rotations and tendencies to rotate.
In my mind, I see a paraphernalia of mathematical tools.
Fine, then along comes this strange operation: norm of the first vector, norm of the...
So I do know that there does exist a generalization of the cross product (the exterior product), but this question does not concern that (and I would prefer it not )
I know that the cross product (that Theodore Frankel, for example, calls "the most toxic operation in math") works in 3D only...
I approach a traffic light. It is red.
I know it is a light.
What is happening in my brain to inform me that I am looking at a red light, and not a brightly colored red circle on the canvas of my perceptions of the physical world?
If my eyes are moist and I squint, I see radiating red lines...
By "real world purpose" I only meant: "can I say to the students: yes, this is an ideal problem to learn the workings of HP, but in THIS particular case, THIS mechanism is also used for this purpose."
But I am beginning to think most of the examples given in textbooks that teach HP, are indeed...
Yes, I know I can build it, but that is not the question.
I see all these examples in a textbook on Hamilton's Principle.
With some of them, I want to motivate the students by saying
"Yes, we could build it, but it would not be purposeful/useful."
I am trying to find out if this mechanism...
Goooood Morning all!
I am going through a few problems in advanced dynamics with Hamilton's Principle.
One of them is shown above (this is NOT a question about the solution)
The spring constants, damping, mass, force, are all given. So, too, is the constraint: large disk rolls without...
Hello
May I begin by saying I do not exactly know what I am asking, but here goes...
In the Finite Element Method (as used in Solid Mechanics), we convert the differential equations of continuum mechanics into integral form. Here, I am thinking of the more pragmatic Principle of Virtual Work...
To carry out the machinery of Hamilton's Principle though the calculus of variations, we desire to vary the position and velocity, independently.
We proceed by varying at action, and set the variation to zero (I will assume ONE generalized variable: q1)
In the above, I can see how we vary...