295 lines
4.1 KiB
Plaintext
295 lines
4.1 KiB
Plaintext
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#LyX 1.6.5 created this file. For more info see http://www.lyx.org/
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\lyxformat 345
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\begin_document
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\author ""
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\author ""
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\begin_inset Note Comment
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status open
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Derivatives
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\end_layout
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\begin_layout Standard
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\begin_inset FormulaMacro
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{\frac{\partial#1}{\partial#2}}
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\begin_inset FormulaMacro
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\newcommand{\at}[2]{#1\biggr\rvert_{#2}}
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{#1\biggr\rvert_{#2}}
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\end_inset
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\begin_inset FormulaMacro
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\newcommand{\Jac}[3]{ \at{\deriv{#1}{#2}} {#3} }
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{\at{\deriv{#1}{#2}}{#3}}
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\end_inset
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\end_layout
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\begin_layout Standard
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\begin_inset Note Comment
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status open
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\begin_layout Plain Layout
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Lie Groups
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\end_layout
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\end_inset
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\end_layout
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\begin_layout Standard
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\begin_inset FormulaMacro
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\newcommand{\xhat}{\hat{x}}
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{\hat{x}}
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\end_inset
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\begin_inset FormulaMacro
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\newcommand{\yhat}{\hat{y}}
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{\hat{y}}
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\end_inset
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\begin_inset FormulaMacro
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\newcommand{\Ad}[1]{Ad_{#1}}
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{Ad_{#1}}
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\end_inset
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\end_layout
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\begin_layout Standard
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\begin_inset FormulaMacro
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\newcommand{\define}{\stackrel{\Delta}{=}}
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{\stackrel{\Delta}{=}}
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\end_inset
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\begin_inset FormulaMacro
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\newcommand{\gg}{\mathfrak{g}}
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{\mathfrak{g}}
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\end_inset
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\begin_inset FormulaMacro
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\newcommand{\Rn}{\mathbb{R}^{n}}
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{\mathbb{R}^{n}}
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\end_inset
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\end_layout
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\begin_layout Standard
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\begin_inset Note Comment
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status open
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\begin_layout Plain Layout
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SO(2)
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\end_layout
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\end_inset
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\end_layout
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\begin_layout Standard
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\begin_inset FormulaMacro
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\newcommand{\Rtwo}{\mathfrak{\mathbb{R}^{2}}}
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{\mathfrak{\mathbb{R}^{2}}}
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\end_inset
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\begin_inset FormulaMacro
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\newcommand{\SOtwo}{SO(2)}
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{SO(2)}
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\end_inset
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\begin_inset FormulaMacro
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\newcommand{\sotwo}{\mathfrak{so(2)}}
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{\mathfrak{so(2)}}
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\end_inset
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\begin_inset FormulaMacro
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\newcommand{\that}{\hat{\theta}}
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{\hat{\theta}}
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\end_inset
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\begin_inset FormulaMacro
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\newcommand{\skew}[1]{[#1]_{+}}
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{[#1]_{+}}
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\end_inset
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\end_layout
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\begin_layout Standard
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\begin_inset Note Comment
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status open
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\begin_layout Plain Layout
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SE(2)
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\end_layout
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\end_inset
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\end_layout
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\begin_layout Standard
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\begin_inset FormulaMacro
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\newcommand{\SEtwo}{SE(2)}
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{SE(2)}
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\end_inset
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\begin_inset FormulaMacro
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\newcommand{\setwo}{\mathfrak{se(2)}}
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{\mathfrak{se(2)}}
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\end_inset
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\end_layout
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\begin_layout Standard
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\begin_inset Note Comment
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status open
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\begin_layout Plain Layout
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SO(3)
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\end_layout
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\end_inset
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\end_layout
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\begin_layout Standard
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\begin_inset FormulaMacro
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\newcommand{\Rthree}{\mathfrak{\mathbb{R}^{3}}}
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{\mathfrak{\mathbb{R}^{3}}}
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\end_inset
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\begin_inset FormulaMacro
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\newcommand{\SOthree}{SO(3)}
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{SO(3)}
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\end_inset
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\begin_inset FormulaMacro
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\newcommand{\sothree}{\mathfrak{so(3)}}
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{\mathfrak{so(3)}}
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\end_inset
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\begin_inset FormulaMacro
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\newcommand{\what}{\hat{\omega}}
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{\hat{\omega}}
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\end_inset
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\begin_inset FormulaMacro
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\newcommand{\Skew}[1]{[#1]_{\times}}
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{[#1]_{\times}}
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\end_inset
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\end_layout
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\begin_layout Standard
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\begin_inset Note Comment
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status open
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\begin_layout Plain Layout
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SE(3)
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\end_layout
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\end_inset
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\end_layout
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\begin_layout Standard
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\begin_inset FormulaMacro
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\newcommand{\Rsix}{\mathfrak{\mathbb{R}^{6}}}
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{\mathfrak{\mathbb{R}^{6}}}
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\end_inset
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\begin_inset FormulaMacro
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\newcommand{\SEthree}{SE(3)}
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{SE(3)}
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\end_inset
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\begin_inset FormulaMacro
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\newcommand{\sethree}{\mathfrak{se(3)}}
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{\mathfrak{se(3)}}
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\end_inset
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\begin_inset FormulaMacro
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\newcommand{\xihat}{\hat{\xi}}
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{\hat{\xi}}
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\end_inset
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\end_layout
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\end_body
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\end_document
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