- #1

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## Main Question or Discussion Point

Can someone please tell me what the first six terms are in the classical expression for kinetic energy.

Thanks,

Ian.

Thanks,

Ian.

- Thread starter Ian
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- #1

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Can someone please tell me what the first six terms are in the classical expression for kinetic energy.

Thanks,

Ian.

Thanks,

Ian.

- #2

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1) The kinetic energy of what?

2) Why did you post this in the**general math** forum?

2) Why did you post this in the

- #3

Njorl

Science Advisor

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E

p=mv

substitute and simplify to E=mc

then use the binomial theorem. The first term of the binomial expansion will be the rest energy, the next term will be the commonly used (1/2)mv

Njorl

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- #5

Njorl

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I agree. I don't think there is a standard terminology for the next few terms of the expansion. I suppose they could be called the first through fifth order corrections to the classical formula for kinetic energy.Originally posted by suyver

Njorl

- #6

ahrkron

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They do not correspond to any named quantity in classical physics.Originally posted by Ian

Can someone please tell me what the first six terms are in the classical expression for kinetic energy.

Thanks,

Ian.

This needs not be surprising. You can write any function as a linear combination of other functions in many ways (much in the way you can use different coordinate systems for describing vectors).

It turns out that, when you expand the K.E. in powers of v/c, you gain some understanding of why things look like classical mechanics when v/c<<1, but the (infinitely many) higher-order terms do not have a wide enough use to get them a name of their own; actually, had relativity not prompted this peculiar expansion of KE in terms of powers of (v/c), those terms would probably never had shown up elsewhere.

- #7

Integral

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I guess for the most part I would simply call them, ignored!

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