Range rate について

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Range rate ：ウィキペディア英語版

Range rate

Given a differentiable vector

\mathbf

\mathbb^3

defining the position of a target relative to an observer.
Let
|}}
The magnitude of the position vector

\mathbf

is defined as
The quantity range rate is the time derivative of the magnitude (norm) of

\mathbf

, expressed as
Substituting () into ()
:

\frac = \frac \rangle^ }

Evaluating the derivative of the right-hand-side
:

\frac = \frac  \frac \rangle}  \frac \rangle^}

\frac = \frac  \frac,\mathbf \rangle + \langle \mathbf,\frac \rangle} \rangle^}

using () the expression becomes
:

\frac = \frac  \frac \rangle+\langle \mathbf,\mathbf \rangle} \rangle^}

Since
:

\langle \mathbf,\mathbf \rangle = \langle \mathbf,\mathbf \rangle

then the range rate is simply defined as
:

\frac = \frac \rangle} \rangle^} = \langle \hat \rangle

the projection of the observer to target velocity vector onto the

\mathbf

unit vector.
==See also==

* inner product
* orbit determination
* Lp space

抄文引用元・出典: フリー百科事典『ウィキペディア（Wikipedia）』
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