Re: Relativistic Dynamics

On Jul 14, 4:26 am, Eric Gisse <jowr...@xxxxxxxxx> wrote:
On Jul 13, 5:02 pm, Dono <sa...@xxxxxxxxxxx> wrote:

On Jul 13, 1:49 am, Eric Gisse <jowr...@xxxxxxxxx> wrote:

On Jul 12, 8:39 pm, Dono <sa...@xxxxxxxxxxx> wrote:

[...]

There are three ways, and yours is the option that nobody should pick..

...except it worked perfectly :-)

No denying that - I just believe it is more effort than it is worth
since there are easier methods.







a) Covariantly: Use the geodesic equation and a four-vector
formulation of the force.
b) Covariantly: Construct the Lagrangian from four-vectors and use a
four-force derivable from a four-potential. Then build a new four-mine
to get new fours, as the world is running out.
c) Not-covariantly: Write the regular Lagrangian -mc^2sqrt[1-v^2/c^2]
and go as normally.

Going with c, I basically get d/dt [mv*gamma] = F. Not _terrifically_
surprising but it is good to know it behaves as expected.

I need some help with the situation when F is NOT constant.
Here are several examples:

1. F= - q*x (common spring)

Maple reduces this to a quadrature that appears to be solvable exactly
if given initial conditions.

I think you missed the point, please read my post again. The problem
is that one cannot get a covariant formulation of the Hooke law
because of the right hand term. What I asked is : how do we need to
modify Hooke's law in order to have a covariant formulation.

My bad - couldn't see the forest for the trees.


No problem, let's move on.

I think you are overthinking what you want to do unless I'm still
missing the point. Why not go with the simplest answer: Write the
force as a four-vector like F = (0, qx, 0, 0) ?

Writing the force as a four-vectors is sufficient to ensure
covariance, imho. Then all you'd have to do is shove it in the right
hand side of the geodesic equation!

I am not sure how this would solve the problem, can you do the
calculations (at least the few starting steps)? so we have a few
equations to look at? I would greatly appreciate this.

.

Relevant Pages

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  • Re: Relativistic Dynamics
    ... and yours is the option that nobody should pick. ... is that one cannot get a covariant formulation of the Hooke law ... modify Hooke's law in order to have a covariant formulation. ...
    (sci.physics.relativity)
  • Re: Relativistic Dynamics
    ... is that one cannot get a covariant formulation of the Hooke law ... modify Hooke's law in order to have a covariant formulation. ... hand side of the geodesic equation! ... metric and U is the four velocity. ...
    (sci.physics.relativity)
  • Re: Difference between predictions of SR and LET - perhaps!
    ... straight questions about the stability and about the covariance of his ... expressible in a covariant formulation. ... I have never said that my theory is not expressible in a covariant ... And I have a non-covariant and a covariant formulation. ...
    (sci.physics.relativity)