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kellyzeissss1286
02.07.2019 •
Mathematics
Gfind the jacobian of the transformation. x = 6e−3r sin 2θ, y = e3r cos 2θ
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Ответ:
Definition:
The Jacobian of the transformation x = f(r, θ) and y = g(r ,θ) is:
Given:
and ![y=e^{3r}\cos 2\theta](/tpl/images/0043/2742/4b546.png)
then,
and
Substitute these value in [1] ;
=![(-18e^{-3r}\sin 2\theta)\cdot(-2e^{3r}\sin 2\theta)-(12e^{-3r}\cos 2\theta)\cdot(3e^{3r}\cos 2\theta)](/tpl/images/0043/2742/ae88e.png)
=![(-18 \cdot -2)e^{-3r+3r} \sin^2 2\theta - (12 \cdot 3)e^{-3r+3r} \cos^2 2\theta](/tpl/images/0043/2742/94f86.png)
On simplify:
=
[ Use
]
therefore, the jacobian transformation of
and
is;
Ответ: