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Topic: Landau & Lifschitz, Mechanics, Principle of Least Action
Replies: 10   Last Post: Jan 19, 2014 8:24 PM

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William Elliot

Posts: 2,637
Registered: 1/8/12
Re: Landau & Lifschitz, Mechanics, Principle of Least Action
Posted: Jan 17, 2014 2:28 AM
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On Wed, 15 Jan 2014, Hetware wrote:

> On page 3 of Landau & Lifschitz's Mechanics it is stated that
> delta q-dot = d(delta q)/dt.

> This fact is not demonstrated, it is asserted. q-dot is a vector /tangent to/
> the particle trajectory. delta-q is a displacement /of/ that trajectory. I
> see no a priori reason to believe the two are interchangeable.

pho = position vector = q
tau = tangent vector = q-dot
tau = dpho/dt

delta tau(t) = tau(t + delta t) - tau(t)
= dpho(t + delta t)/dt - dpho(t)/dt
= d(pho(t + delta t) - pho(t))/dt
= d(delta pho(t))/dt

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