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Trying2Learn
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- Differential to Integral Equations
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, rather that exploiting the more mathematically sophisticated strong/weak formulations (but no matter on that detail)
In Hamilton's Principle, we reformulate Newtonian Dynamics into Analytical Dynamics, but extremizing the Action of the Lagrangian.
Now, in both cases, we convert differential equations into integral equations.
So something is happening here... this act of converting differential into integral. Through the haze of my confusion I can sort of see that the result is more easily addressed with computer programming
Could someone elaborate, perhaps a bit more philosophically, on what is happening when we do these things.
In one sense, both processes relate to variational methods, but is something going on here that these two approaches (sort of) resemble each other, in a way)?
Or am I thinking a bit silly?
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, rather that exploiting the more mathematically sophisticated strong/weak formulations (but no matter on that detail)
In Hamilton's Principle, we reformulate Newtonian Dynamics into Analytical Dynamics, but extremizing the Action of the Lagrangian.
Now, in both cases, we convert differential equations into integral equations.
So something is happening here... this act of converting differential into integral. Through the haze of my confusion I can sort of see that the result is more easily addressed with computer programming
Could someone elaborate, perhaps a bit more philosophically, on what is happening when we do these things.
In one sense, both processes relate to variational methods, but is something going on here that these two approaches (sort of) resemble each other, in a way)?
Or am I thinking a bit silly?
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