Search type Search syntax
Tags [tag]
Exact "words here"
Author user:1234
user:me (yours)
Score score:3 (3+)
score:0 (none)
Answers answers:3 (3+)
answers:0 (none)
isaccepted:yes
hasaccepted:no
inquestion:1234
Views views:250
Code code:"if (foo != bar)"
Sections title:apples
body:"apples oranges"
URL url:"*.example.com"
Saves in:saves
Status closed:yes
duplicate:no
migrated:no
wiki:no
Types is:question
is:answer
Exclude -[tag]
-apples
For more details on advanced search visit our help page
Results tagged with
Search options not deleted user 231957

Classical mechanics discusses the behaviour of macroscopic bodies under the influence of forces (without necessarily specifying the origin of these forces). If it's possible, USE MORE SPECIFIC TAGS like [newtonian-mechanics], [lagrangian-formalism], and [hamiltonian-formalism].

53 votes
7 answers
11k views

Why does Taylor’s series “work”?

I am an undergraduate Physics student completing my first year shortly. The following question is based on the physical systems I’ve encountered so far. (We mostly did Newtonian mechanics.) In all of …
  • 1,843
2 votes
0 answers
64 views

"The state-space for a single particle in classical space is 6-dimensional" -- Is this wrong?

The general argument is as follows. By Newton's second law $\mathbf F=m\ddot{\mathbf{x}}$. Now it is said that this is a second-order ODE and hence requires $\mathbf x(0)$ and $\mathbf{\dot{x}}(0)$ as …
  • 1,843
1 vote
1 answer
49 views

Is a trajectory connecting two points valid for all the intermediate points too?

Suppose a particle is described by a Lagrangian $\mathcal L(q_i, \dot{q_i}, t)$. Suppose that $q_i(t)$ is a trajectory (there might be more that one) along which the action integral is stationary for …
  • 1,843
1 vote
0 answers
15 views

Is there a minimization principle for Hamiltonian? [duplicate]

Consider a point particle in $n$ dimensions. For a Lagrangian $\mathcal L(\mathbf{q, \dot q}, t)$, we have that $\mathbf q(t)$ is a feasible trajectory for times $t_0<t<t_f$ iff it extremizes the inte …
  • 1,843
3 votes
1 answer
119 views

How does the Lagrangian transform when coordinates are changed?

I'll talk of single particle Lagrangian in $n$ dimensions. Suppose in a given coordinate system with the coordinates $(q_i)_{i=1}^n$, the Lagrangian is given by $L(\mathbb{q, \dot q}, t)$. Suppose I …
  • 1,843
0 votes
1 answer
123 views

What is a mathematically precise definition of mass in Lagrangian mechanics?

This is a question on Lagrangian formulation of mechanics and not Newton's formulation. So, we don't a priori take Newton's laws to be true. This SE post has answers which brilliantly define mass expl …
  • 1,843
2 votes
1 answer
63 views

I don't get this "derivation" of canonical transformation

Given a transformation $$(q, p, t)\to (Q(q, p, t), P(q, p, t), t),$$ the modified Hamiltonian, $K$ is related to the original one, $H$, as $$H(q, p, t) = K(Q(q, p, t), P(q, p, t), t).$$ Now, what I've …
  • 1,843
0 votes
1 answer
380 views

Are Poisson brackets preserved during a canonical transformation?

Fix a Hamiltonian $H(q, p, t)$. Definition: A transformation $(q, p, t)\mapsto (Q(q, p, t), P(q, p, t), t)$ is said to be canonical iff for the Kamiltonian $K$ defined as $H(q, p, t)=K(Q(q, p, t), P(q …
  • 1,843