# What is Hamilton: Definition and 74 Discussions

Hamilton: An American Musical is a sung-and-rapped-through musical by Lin-Manuel Miranda. It tells the story of American Founding Father Alexander Hamilton. Miranda said he was inspired to write the musical after reading the 2004 biography Alexander Hamilton by Ron Chernow. The show draws heavily from hip hop, as well as R&B, pop, soul, and traditional-style show tunes. It casts non-white actors as the Founding Fathers and other historical figures. Miranda described Hamilton as about "America then, as told by America now".From its opening, Hamilton received critical acclaim. It premiered Off-Broadway on February 17, 2015, at the Public Theater, with Miranda playing the role of Alexander Hamilton, where its several-month engagement was sold out. The musical won eight Drama Desk Awards, including Outstanding Musical. It then transferred to the Richard Rodgers Theatre on Broadway, opening on August 6, 2015, where it received uniformly positive reviews and high box office sales. At the 70th Tony Awards, Hamilton received a record-breaking 16 nominations and won 11 awards, including Best Musical. It received the 2016 Pulitzer Prize for Drama. A filmed version of the Broadway production was released in 2020 on Disney+.
The Chicago production of Hamilton began preview performances at the CIBC Theatre in September 2016 and opened the following month. The West End production opened at the Victoria Palace Theatre in London on December 21, 2017, following previews from December 6 and winning seven Olivier Awards in 2018, including Best New Musical. The first U.S. national tour began in March 2017. A second U.S. tour opened in February 2018. Hamilton's third U.S. tour began January 11, 2019, with a three-week engagement in Puerto Rico in which Miranda returned to the role of Hamilton.

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1. ### I How did Hamilton derive the characteristic function V in his essay?

In Hamilton's "on a general method in dynamics", he starts with varying the function ##U## and writes the equation: $$\delta U=\sum m(\ddot x\delta x+\ddot y\delta y+\ddot z\delta z)$$ Then he defines ##T## to be: $$T=\frac{1}{2}\sum m (\dot x^2+\dot y^2+\dot z^2)$$ Then by ##dT=dU##, he...
2. ### Margaret Hamilton, Lead Programmer, Apollo Program's Guidance Computer

Margaret Hamilton the Pioneering Software Engineer Who Saved the Moon Landing https://interestingengineering.com/margaret-hamilton-software-engineer-who-saved-the-moon-landing Margaret Hamilton began working with Edward Lorenz, the father of Chaos Theory, in MIT's meteorology department. As...
3. ### Anyone know a reactor physics book better than Duderstadt and Hamilton?

I really like the book for how much it covers. There's not a single topic that's missed that is relevant to nuclear reactor design/analysis. Often other books can miss a topic or two. It's just that the style is not to the point and often time is wasted talking about things that are irrelevant...
4. ### A simple pendulum is suspended from the ceiling of an accelerating car

Here is an image of the problem: The problem consist in finding the moviment equation for the pendulum using Lagrangian and Hamiltonian equations. I managed to get the equations , which are shown insed the blue box: Using the hamilton equations, i finally got that the equilibrium angle...
5. ### A Why do we extremize the Lagrangian in the Hamilton principle instead of energy?

I know that by extremizing lagrangian we get equations of motions. But what if we extremize the energy? I am just little bit of confused, any help is appreciated.
6. ### A Help on some equations in Einstein's original papers

Studying Einstein's original Die Grundlage der allgemeinen Relativitätstheorie, published in 1916's Annalen Der Physik, I came across some equations which I couldn't verify after doing the computations hinted at. The first are equations 47b) regarding the gravity contribution to the...
7. ### Heisenberg and Varying the Velocity

Good Morning When we derive the Euler Lagrange equations using Hamilton's Principle, we make a point of varying the velocity and the position at the same time, (despite the fact that, normally, they are related through a derivative). I do understand that this is allowed: we are trying to find...
8. ### A The tautological 1-form: Lagrange vs. Hamilton formalism

Classical mechanics is based on conservation laws which represent the symmetries of spacetime. The lagrangian function L is a function of position and velocity while the hamiltonian is a function of position and momentum. The velocity and momentum descriptions are related by a legendre...
9. ### I Hamilton path and circuit rounded path problem

Here is a graph. I wonder if it has hamilton path or circuit. In hamilton path we have to cross once and only once at an edge, and the start and the finish must be different locations. In hamilton circuit we have to start and finish the same edge. So the circle which B is rounded, which kind of...
10. ### Hamilton Jacobi equation for time dependent potential

Homework Statement Suppose the potential in a problem of one degree of freedom is linearly dependent upon time such that $$H = \frac{p^2}{2m} - mAtx$$ where A is a constant. Solve the dynamical problem by means of Hamilton's principal function under the initial conditions t = 0, x = 0, ##p =...
11. ### Prove that ##\psi## is a solution to Schrödinger equation

Homework Statement For a wavefunction ##\psi##, the variance of the Hamiltonian operator ##\hat{H}## is defined as: $$\sigma^2 = \big \langle \psi \mid (\hat{H} - \langle\hat{H}\rangle)^2 \psi \big\rangle$$ I want to prove that if ##\sigma^2 = 0##, then ##\psi## is a solution to the...
12. ### A Canonical transformation - derviation problem

Let me show you part of a book "Mechanics From Newton’s Laws to Deterministic Chaos" by Florian Scheck. I do not understand why these integrands can differ by more than time derivative of some function M. Why doesn't it change the value of integrals? It seems this point is crucial for me to...
13. ### Hamilton - Jacobi method for a particle in a magnetic field

Homework Statement Hamiltonian of charged particle in magnetic field in 2D is ##H(x,y,p_x,p_y)=\frac{(p_x-ky)^2+(p_y+kx)^2}{2m}## where ##k## and ##m## are constant parameters. For separation of this system use ##S=U(x)+W(y)+kxy+S_t(t)##. Solve Hamilton - Jacobi equation to get ##x(t), y(t)## ...
14. ### A EoM in Schwarzschild geometry: geodesic v Hamilton formalism

Hi there guys, Currently writing and comparing two separate Mathematica scripts which can be found here and also here. The first one I've slightly modified to suit my needs and the second one is meant to reproduce the same results. Both scripts are attempting to simulate the trajectory of a...
15. ### Hamilton equation for a block on an inclined plane

Homework Statement I am asked to find the Hamilton equations for a block on an inclined plane (no friction) Homework EquationsThe Attempt at a Solution Please ignore the fact that my steps are written in French (sorry!) I am no longer sure of what I'm doing when it comes to finding the...
16. ### A Ising model and Hamilton function

In case of Ising model we are working with effective Hamiltonian. So let's look to spins which interact. In a case of feromagnet energy function is defined by ## H=-JS_1S_2 ## We have two possibilities. ##S_1## and ##S_2## has different values. And ##S_1## and ##S_2## has the same value. In...
17. ### A Lagrange vs Hamilton: Clarifying the Distinction

Hello, When doing a little internet search today on generalized coordinates I stumbled on this document: http://people.duke.edu/~hpgavin/cee541/LagrangesEqns.pdf If you are willing, would you be so kind as to open it up and look at the top of (numbered) page 6? OK, so the very existence of...
18. ### A Generalized Coordinates and Porn

Yes, that is a serious title for the thread. Could someone please define GENERALIZED COORDINATES? In other words (and with a thread title like that, I damn well better be sure there are other words ) I understand variational methods, Lagrange, Hamilton, (and all that). I understand the...
19. ### 1-D Lagrange and Hamilton equation gives different results.

Homework Statement This was supposed to be an easy question. I have a question here that wants you to describe a yoyo's acceleration (in one dimension) using Lagrangian mechanics. I did and got the right answer. Now I want to use Hamilton's equations of motion but I get a wrong number. Here is...
20. ### I Understanding Hamiltonian Conservation Laws

I'm a little confused about the hamiltonian. Once you have the hamiltonian how can you find conserved quantities. I understand that if it has no explicit dependence on time then the hamiltonian itself is conserved, but how would you get specific conservation laws from this? Many thanks

22. ### Hamiltonian Optics Basics: Explained for Beginners

Alright I was browsing through feynman's lectures VOL.1 When I came across Hamiltonian Optics I am not quite able to understand it in its entirety Could someone explain the basics of hamiltonian optics to me Help would be much appreciated !
23. ### Hamilton Operator for particle on a circle -- Matrix representation....

Hey JO. The Hamiltonian is: H= \frac{p_{x}^{2}+p_{y}^{2}}{2m} In quantum Mechanics: \hat{H}=-\frac{\hbar^{2}}{2m}(\frac{\partial^{2}}{\partial x^{2}}+\frac{\partial^{2}}{\partial x^{2}}) In polar coordinates: \hat{H}=-\frac{\hbar^{2}}{2m}( \frac{\partial^{2}}{\partial r^{2}}+\frac{1}{r}...
24. ### Hamilton EOM for Schwarzschild Metric: Problem Solved

I have a problem (this is not homework) Based on covariant Lagrangian ## \mathcal {L} = \frac {m}{2} \frac{dx^{\mu}}{ds} \frac {dx _ {\mu}}{ds} ## record the equations of motion in Hamiltonian form for a particle in the Schwarzschild metric (SM). Based on Legandre transformations...
25. ### How Does the Hamilton-Jacobi Equation Describe Particle Motion in a Plane?

Homework Statement The motion of a free particle on a plane has hamiltonian $$H =E = \text{const} = \frac{1}{2m} (p_r^2 + \frac{p_{\theta}^2}{r^2})$$ Set up and find a complete integral for ##W##, the time independent generating function to canonical coordinates such that new coordinates are...
26. ### Obtain Equation Using Hamilton's Principle

I want to obtain equation using Hamilton principle but I just couldn't figure it out; i have The kinetic energy : E_{k}=\dfrac{1}{2}m_{z} \displaystyle\int\limits_{0}^{L}\ \left[ \left( \dfrac{\partial w(x,t)}{\partial t}\right)^{2}+\left( \dfrac{\partial v(x,t)}{\partial...
27. ### Verifying Duderstadt & Hamilton's Eqs. (4-134) & (4-137) in Nuclear Transport

Show by direct calculation that Eqs. (4-134) and (4-137) in the textbook by Duderstadt and Hamilton hold, i.e.:(a) ∫ dΩΩiΩj= 4π/3 δij; i,j = x,y,z; 4π(b) ∫ dΩΩxΩyΩz = 0, if l, m, or n is odd. 4π The integrals are over 4π. This is part of the derivation of the diffusion equation...
28. ### Casual talk. Constrained Hamilton systems. Dirac brackets.

Casual talk. Constrained Hamilton systems. Dirac-Poisson brackets. Casual talk. Constrained Hamilton systems. Dirac-Poisson brackets. Hi guys, I think I have finally succeeded in understanding the ideas which Dirac explained in the two first chapters of his book "Lectures on Quantum...
29. ### What are the Hamilton equations of motion

Definition/Summary Hamilton's equations of motion is a very general equation of a system evolving deterministically in phase space. Equations \left( {\begin{array}{*{20}{c}} {\dot q}\\ {\dot p} \end{array}} \right) = \left( {\begin{array}{*{20}{c}} 0&1\\ { - 1}&0 \end{array}}...
30. ### Question about the Hamilton Jaccobi Equation

Hi, I was wondering about the interpretation of the Hamilton Jaccobi equation. Naively we have H + \partialS/\partialt = 0 where H is the Hamiltonian and S is the action. But the action is the time integral of the Lagrangian so you would expect \partialS/\partialt = L Thus H + L = KE +...
31. ### Why is the Cayley-Hamilton theorem important for matrices?

Given a Matrix A = [a,b;c,d] and it's characteristic polynomial, why does the characteristic polynomial enables us to determine the result of the Matrix A raised to the nth power?
32. ### Hamilton Equation and Heisenberg Equation of Motion

I was given the (general) following form for the Hamilton and Heisenberg Equations of motion \dot{A} = (A, H)_{}, which can represent the Poisson bracket (classical version) or \dot{A} = -i/h[A,H] (Quantum Mechanical commutator). I was given the general solutin for A(t) = e^{tL}A...
33. ### Cayley - Hamilton Theorem on higher powers

Homework Statement Given the following matrix A = [3 -1; -1 3] Find C = (0.5*A - I)100 Homework Equations Using the knowledge that the Cayley - Hamilton Theorem must satisfy its own characteristic polynomial. The Attempt at a Solution Here the characteristic polynomial is λ2 -...
34. ### Prob/Stats Time Series Analysis by Hamilton

Author: James Douglas Hamilton Title: Time Series Analysis Amazon Link: https://www.amazon.com/dp/0691042896/?tag=pfamazon01-20
35. ### Lagrange vs Hamilton: What's the Difference?

if lagrangian mechanics is available the why we needed hamiltonian mechanics. where they differ from each other?
36. ### MHB How to show a graph contains no Hamilton cycles?

Here is the graph in question: The edges in red are the paths that must be included in the cycle, since vertices a, k, e, and o have only degree 2. I listed all possible routes starting from vertex b, and showed that they all routes closes a cycle while leaving some vertex disconnected. Is...
37. ### MHB Finding Hamilton Cycles by hand

I know there are no algorithms for finding one, but what are some guidelines? One tip I came up with is that if you have a vertex with degree 2, there is only one way to go through that vertex. Are there any others?
38. ### What are the hamilton equations of motion for homogeneous lagrangians?

For a Lagrangian L(x^k,\dot{x}^k) which is homogeneous in the \dot{x}^k in the first degree, the usual Hamiltonian vanishes identically. Instead an alternative conjugate momenta is defined as y_j=L\frac{\partial L}{\partial \dot{x}^j} which can then be inverted to give the velocities as a...
39. ### How go from Langevin to Hamilton

I have a system described by the Langevin equation da/dt = - dF/da* + r where a are complex amplitudes of electromagnetic modes (and r is the white noise). How if F was real, it would be the Hamiltonian of the system, but in my case (and in general), F is complex (because the a are...
40. ### Cayley Hamilton Theorem

In my linear algebra course, we just finished proving the cayley hamilton theorem (if p(x) = det (A - xI), then p(A) = 0). The theorem seems obvious: if you plug in A into p, you get det (A-AI) = det (0) = 0. But, of course, you can't do that (this is especially clear when you consider what...
41. ### Importance of constrained Hamilton dynamics and BRST transformations

(First of all apologies for the long wall of text) I am to study BRST transformations, for which I'm currently trying to understand constrained Hamiltonian dynamics to treat systems with singular Lagrangians. The crude recipe followed is Lagrangian -> Hamiltonian -> Dirac brackets and their...
42. ### Understanding the Hamilton-Jacobi Equation in Conservative Systems

Hello! General Question about the H-J equation. What are the steps to be followed if we are in a conservative system? And while answering my question, please in the step after we find S, and when you derive S wrt alpha and place it equals to β. When is alpha Energy? When it is not? i.e is it...
43. ### Centre of the real Hamilton Quaternions H

Can anyone help me with the following exercise from Dummit and Foote? ============================================================ Describe the centre of the real Hamilton Quaternions H. Prove that {a + bi | a,b R} is a subring of H which is a field but is not contained in the centre...
44. ### Hamilton operator with moments of inertia : time - independence

Homework Statement The Hamilton-operator is given as \hat{H} and describes the movement of a free rigid object that has the moments of inertia I_{i} Under what circumstances is <\Psi|\hat{L_{1}}|\Psi> time-independent? Homework Equations...
45. ### Hamilton function of a free particle/Landau's book

Homework Statement The problem is taken out of Landau's book on classical mechanics. I must find the Hamilton function and the corresponding Hamilton equations for a free particle in Cartesian, cylindrical and spherical coordinates.Homework Equations Hamilton function: H(p,q,t)= \sum p_i \dot...
46. ### Getting lorentz electromagnetic force from hamilton principle

the title is pretty clear, so we have this F=q( E+V/c X B) the force for a point charge q in an electromagnetic field. and we have the formula to the hamiltonian of electromag force: H= (P+ q/c.A)/2m _ e\phi. the question is how can I get the F from the hamilton principle, using the...
47. ### What are Some Real-Life Applications of the Cayley Hamilton Theorem?

Are there any nice applications of the Cayley Hamilton Theorem. I am looking for a real life application which would motivate students.
48. ### Jacobi least time vs. Fermat Hamilton

Could anyone give me a simple explanation as to why the Fermat/Hamilton principle would be called more general than the Jacobi least time principle? I am trying to understand what differences would result from using the one principle vs. the other; eg: where/in what way would the Jacobi least...
49. ### Diagonalizable Hamilton denisty?

Homework Statement I'm working with a complex scalar field with the lagrange density L= \partial_{\mu} \phi^{\ast} \partial^{\mu} \phi - m^2 \phi^{\ast} \phi And I've shown that's its hamilton density H= \int d^3 x ( \pi^{\ast} \pi + \nabla \phi^{\ast} \cdot \nabla \phi + m^2 \phi^{\ast}...
50. ### DearsIs there any similar equation (in Lamarsh or hamilton books)

Dears Is there any similar equation (in Lamarsh or hamilton books) like the one in the attached picture(equation1)? From where R. Serber derived this one? Best regards