[comment_ran]

It descripts a system using the energy concept. The total energy of the system, which is the sum of kinetic energy and potential energy. Its formula often looks like H = T + V, where T represents kinetic energy and V represents potential energy.

Both the quantum mechanics and molecular dynamics have shared a similar concept.

In structural mechanics, we use the virtual method to calculate the hyperstatic structure to determine displacements in a structure, given forces acting on the structure. Another kind of Hamiltonian.

[tekla]

I'm classically educated on fluids so asking me to deviate from Newtonian mechanics for viscous fluids is ... difficult.

Nothing against this tho, I just don't have the foundation for this.

[spenczar5]

I am curious about what you mean by “classically educated.” In my undergrad physics education, computing Hamiltonians was pretty much an entire semester of classical mechanics in my junior year.

We didn’t really touch fluids though. Does “classical” mean something different there?

[kyykky]

I assume that the classical exposition to fluid mechanics uses newtonian concepts, mainly forces.

[comment_ran]

I still remember in high school, we only need two or three equations to solve a free-fall problem. In another book, basically the same question, but someone uses Hamiltonian framework to solve really complex PDEs and couple pages with those crazy equations to basically solve the same thing, and eventually got the same results.

I still remember that was mind-blowing. High school physics is so simple, whereas the Hamilton is so complex. I later on notice that Hamilton is kind of a more standard way to solve the problem. Never mind, I'm not an expert on it, but I'm just kind of amazed by the Hamiltonian mechanics.

[jfengel]

The Hamiltonian is a lot more flexible with respect to frame. The Newtonian formulation works great for simple cases but as it gets more complex it's harder and harder to pick a reference frame that's easy to compute.

Effectively, by working with energy rather than force, you can avoid working with vectors. That ends up being simpler as the components add up.