Recent content by Ben Geoffrey

Sir my question is more along the lines of we write GTR in tensor notation right ? so if we write Lorentz transformation matrix in tensor notation does it mean we've combined STR and GTR and written it as one theory ?

Thank you for that. I have another question. If its a tensor then can we say its written in covariant formulation ? Is there anything like a GTR formulation of STR ?

Is the Lorentz transformation matrix Λμν a tensor of order two and does it transform like a tensor ?

So its like the order of a differential equation ? y multiplied by y' . will have an order 2 ?

could you explain that part a little more ? what is the derivative of n ? and how does multiplying with n make it quadratic in n ? I understand if you multiply two same linear terms like x and x they become quadratic. But how come in this case ?

Can you see I've understood it right, if x is displacement, in small oscillation problem we take x = xo + η where xo initial position is made to coincide with origin and hence becomes zero and there we have only the small displacement η . Now when substituting the first order Taylor...

No my doubt is x times derivative of x, will become x2 ?

No but derivative of n is quadratic and n is linear, if we multiply both we we would get derivative of n square times n right ?

Can you tell me how the linear term in n becomes cubic when substituted in equation 6.5 ? Appreciate your patience in dealing with amateurs

Can anyone tell me how if the derivative of n(n') is quadratic the second term in the taylor series expansion given below vanishes. This doubt is from the book Classical Mechanics by Goldstein Chapter 6 page 240 3rd edition. I have attached a screenshot below

thank you

But why is the variation due to ends points L(t2)Δt2 - L(t1)Δt1 rather than L(t2 +Δt2) - L(t1 +Δt1) . Makes more sense if it is L(t2 +Δt2) - L(t1 +Δt1)

This is with regard to my doubt in the derivation of the principle of least of action in Goldstein Is there any theorem in math about definite integrals like this ∫a+cb+df(x)dx = f(a)c-f(b)d The relevant portion of the derivation is given in the image.

This is the original matrix. So I just transpose it and the rows become columns and columns become rows.

Okay Thanks for the guidance. So The results he gets are in the picture names 'Physics forums' and he says he gets them by inverting this equation show in the picture 'Physics forum 1'. I inverted the aij matrix to aji since it is an orthogonal matrix. But I am not getting the same answers. Can...