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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].

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 …
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### "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 …
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1 vote
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### 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 …
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1 vote
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### 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 …
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### 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 …
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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 …
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### 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 …
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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 …