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# [Phys-L] relativistic acceleration of an extended object

• From: John Denker <jsd@av8n.com>
• Date: Sun, 26 Oct 2014 02:54:38 -0700

Hi --

I posted some notes and diagrams on the subject:
https://www.av8n.com/physics/hyperbolic-motion.htm

Suppose we have an object with some large length (L) undergoing a
large constant acceleration (a). We consider the relativistic case,
where La/c^2 is not small compared to unity.

It is well known that the world-line of pointlike object undergoing
constant acceleration is a hyperbola. When we generalize to a larger
object, we find a few features that may seem non-obvious at first,
but can be given a simple interpretation in terms of the geometry of
spacetime. We call particular attention to the geometrical /center/ of
the hyperbolas.

We shall see that in order for the object to maintain its shape,
different parts will need to accelerate at different rates. This can
be considered a generalization of the notion of centrifugal force, as
applied to the case of a rotation in the xt plane.

Contents

1 Introduction

2 A Numerical Example : Hyperbolic Motion
2.1 Cluster of Pointlike Objects
2.2 Rigid Extended Object

3 Discussion
3.1 Center of the Parabolas
3.2 Centrifugal Stress
3.3 The Relativistic Criteria

4 References

For the rest of the story, see
https://www.av8n.com/physics/hyperbolic-motion.htm

This is new and probably full of typos. Comments, questions, and
suggestions are welcome.