Communities

Writing
Writing
Codidact Meta
Codidact Meta
The Great Outdoors
The Great Outdoors
Photography & Video
Photography & Video
Scientific Speculation
Scientific Speculation
Cooking
Cooking
Electrical Engineering
Electrical Engineering
Judaism
Judaism
Languages & Linguistics
Languages & Linguistics
Software Development
Software Development
Mathematics
Mathematics
Christianity
Christianity
Code Golf
Code Golf
Music
Music
Physics
Physics
Linux Systems
Linux Systems
Power Users
Power Users
Tabletop RPGs
Tabletop RPGs
Notifications
Mark all as read
Q&A

Post History

60%
+1 −0
#2: Post edited by user avatar deleted user · 2021-09-08T16:30:03Z (about 1 year ago)
  • $$F=F(q,p,t)$$
  • $$\frac{dF}{dt}=\frac{\partial F}{\partial q}\frac{\partial q}{\partial t}+\frac{\partial F}{\partial p}\frac{\partial p}{\partial t}+\frac{\partial F}{\partial t}$$
  • $$=\frac{\partial F}{\partial q}\dot{q}+\frac{\partial F}{\partial p}\dot{p}+\frac{\partial F}{\partial t}$$
  • $$=\frac{\partial F}{\partial q}\frac{\partial H}{\partial p}-\frac{\partial F}{\partial p}\frac{\partial H}{\partial x}+\frac{\partial F}{\partial t}$$
  • $$=\\{F,H\\}+\frac{\partial F}{\partial t}$$
  • Here $H$ is Hamilton. And, {F,H} they are inside Poisson braces. My question is what's the importance of Poisson brace? Does everyone use Poisson braces to make equation shorter? It is possible to derive earlier equation from the Poisson braces. Or, is there something else which can be expressed using only Poisson braces?
  • $$F=F(q,p,t)$$
  • $$\frac{dF}{dt}=\frac{\partial F}{\partial q}\frac{\partial q}{\partial t}+\frac{\partial F}{\partial p}\frac{\partial p}{\partial t}+\frac{\partial F}{\partial t}$$
  • $$=\frac{\partial F}{\partial q}\dot{q}+\frac{\partial F}{\partial p}\dot{p}+\frac{\partial F}{\partial t}$$
  • $$=\frac{\partial F}{\partial q}\frac{\partial H}{\partial p}-\frac{\partial F}{\partial p}\frac{\partial H}{\partial x}+\frac{\partial F}{\partial t}$$
  • $$=\\{F,H\\}+\frac{\partial F}{\partial t}$$
  • Here $H$ is Hamilton. And, {F,H} they are inside Poisson braces. My question is what's the importance of Poisson brace? Does everyone use Poisson braces to make equation shorter? It is possible to derive earlier equation from the Poisson braces. Or, is there something else which can be expressed using only Poisson braces? Recently figured out a thing which is if a function (not sure if that's called function rather than variable) is constant than poisson brackets will be 0.
  • I meant if $F$ is constant in $\\{F,H\\}$ then $\\{F,H\\}=0$
#1: Initial revision by user avatar deleted user · 2021-09-08T15:42:27Z (about 1 year ago)
What's the importance of Poisson brackets?
$$F=F(q,p,t)$$
$$\frac{dF}{dt}=\frac{\partial F}{\partial q}\frac{\partial q}{\partial t}+\frac{\partial F}{\partial p}\frac{\partial p}{\partial t}+\frac{\partial F}{\partial t}$$
$$=\frac{\partial F}{\partial q}\dot{q}+\frac{\partial F}{\partial p}\dot{p}+\frac{\partial F}{\partial t}$$
$$=\frac{\partial F}{\partial q}\frac{\partial H}{\partial p}-\frac{\partial F}{\partial p}\frac{\partial H}{\partial x}+\frac{\partial F}{\partial t}$$
$$=\\{F,H\\}+\frac{\partial F}{\partial t}$$

Here $H$ is Hamilton. And, {F,H} they are inside Poisson braces. My question is what's the importance of Poisson brace? Does everyone use Poisson braces to make equation shorter? It is possible to derive earlier equation from the Poisson braces. Or, is there something else which can be expressed using only Poisson braces?