I'm looking at page 94 here - I understand the definition of Poisson brackets at the top of the page (which uses summation convention) but I don't get why the calculations in (4.61) are true. I'm substituting in the generalised coordinate $q_i$ as $f$ and the generalised momentum $p_i$ as $g$, but I must be doing something wrong - do the subscripts in (4.61) not correspond to the subscripts in the definition?
2026-03-31 09:06:04.1774947964
Trouble understanding Poisson Brackets
346 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in PARTIAL-DERIVATIVE
- Equality of Mixed Partial Derivatives - Simple proof is Confusing
- Proving the differentiability of the following function of two variables
- Partial Derivative vs Total Derivative: Function depending Implicitly and Explicitly on Variable
- Holding intermediate variables constant in partial derivative chain rule
- Derive an equation with Faraday's law
- How might we express a second order PDE as a system of first order PDE's?
- Partial derivative of a summation
- How might I find, in parametric form, the solution to this (first order, quasilinear) PDE?
- Solving a PDE given initial/boundary conditions.
- Proof for f must be a constant polynomial
Related Questions in MATHEMATICAL-PHYSICS
- Why boundary conditions in Sturm-Liouville problem are homogeneous?
- What is the value of alternating series which I mention below
- Are there special advantages in this representation of sl2?
- Intuition behind quaternion multiplication with zero scalar
- Return probability random walk
- "Good" Linear Combinations of a Perturbed Wave Function
- Yang–Mills theory and mass gap
- Self adjoint operators on incomplete spaces
- Algebraic geometry and algebraic topology used in string theory
- Compute time required to travel given distance with constant acceleration and known initial speed
Related Questions in CLASSICAL-MECHANICS
- An underdetermined system derived for rotated coordinate system
- Bouncing ball optimization
- Circular Motion Question - fully algebraic
- How can I solve this pair of differential equations?
- How to solve $-\frac{1}{2}gt^2\sin \theta=x$ when $x$ equals $0$
- Find the acceleration and tension in pulley setup
- Derive first-order time derivatives in a second-order dynamic system
- Phase curves of a spherical pendulum
- Velocity dependent force with arbitrary power
- An explanation for mathematicians of the three-body problem using a simple example, and the moons of Saturn
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?