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Tensors and Relativity: Chapter 2

Four- acceleration

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The four- acceleration  of a particle is defined as

eqnarray1027

since

eqnarray1035

we have

equation1041

For speeds much less than the speed of light tex2html_wrap_inline1341 , we obtain

equation1053

therefore spatial part approximates the usual three- acceleration at low velocities.

Note that tex2html_wrap_inline1423 , so the four- acceleration is orthogonal to the four- velocity.

Finally Newtons second law requires that we define the four- force   as

equation1071

 


 

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