Brachistochrone curve
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Determine the necessary conditions of optimum to bring the boat from point 1 $(0,0)$ to point 2 $(x,y)$ for a minimum time, $y$ isn't specified.
Equation for fluid:
$$ s(x)=-frac{2}{625} x^2 + frac{8}{25}x $$
Plot[-fluid, {x, -100, 150},
AspectRatio -> Automatic, {PlotRange -> All}]
FindRoot[fluid, {x, 99}]
Doing this in Math I got that width of a fluid is $100$ so I know the coordinate $x$ of 2nd point.
The boat is traveling with $v=mathrm{const}$ and $beta$ is the angle between $v$ and positive $x$ axis.
Can you help me to solve this?
https://imgur.com/S2klpTS
dynamical-systems kinematics
edited 2 days ago
rafa11111
956417
asked 2 days ago
Aleksić Željko
1
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Aleksić Željko is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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up vote
-2
down vote
favorite
Determine the necessary conditions of optimum to bring the boat from point 1 $(0,0)$ to point 2 $(x,y)$ for a minimum time, $y$ isn't specified.
Equation for fluid:
$$ s(x)=-frac{2}{625} x^2 + frac{8}{25}x $$
Plot[-fluid, {x, -100, 150},
AspectRatio -> Automatic, {PlotRange -> All}]
FindRoot[fluid, {x, 99}]
Doing this in Math I got that width of a fluid is $100$ so I know the coordinate $x$ of 2nd point.
The boat is traveling with $v=mathrm{const}$ and $beta$ is the angle between $v$ and positive $x$ axis.
Can you help me to solve this?
https://imgur.com/S2klpTS
dynamical-systems kinematics
edited 2 days ago
rafa11111
956417
asked 2 days ago
Aleksić Željko
1
New contributor
Aleksić Željko is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
up vote
-2
down vote
favorite
up vote
-2
down vote
favorite
Determine the necessary conditions of optimum to bring the boat from point 1 $(0,0)$ to point 2 $(x,y)$ for a minimum time, $y$ isn't specified.
Equation for fluid:
$$ s(x)=-frac{2}{625} x^2 + frac{8}{25}x $$
Plot[-fluid, {x, -100, 150},
AspectRatio -> Automatic, {PlotRange -> All}]
FindRoot[fluid, {x, 99}]
Doing this in Math I got that width of a fluid is $100$ so I know the coordinate $x$ of 2nd point.
The boat is traveling with $v=mathrm{const}$ and $beta$ is the angle between $v$ and positive $x$ axis.
Can you help me to solve this?
https://imgur.com/S2klpTS
dynamical-systems kinematics
edited 2 days ago
rafa11111
956417
asked 2 days ago
Aleksić Željko
1
New contributor
Aleksić Željko is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Determine the necessary conditions of optimum to bring the boat from point 1 $(0,0)$ to point 2 $(x,y)$ for a minimum time, $y$ isn't specified.
Equation for fluid:
$$ s(x)=-frac{2}{625} x^2 + frac{8}{25}x $$
Plot[-fluid, {x, -100, 150},
AspectRatio -> Automatic, {PlotRange -> All}]
FindRoot[fluid, {x, 99}]
Doing this in Math I got that width of a fluid is $100$ so I know the coordinate $x$ of 2nd point.
The boat is traveling with $v=mathrm{const}$ and $beta$ is the angle between $v$ and positive $x$ axis.
Can you help me to solve this?
https://imgur.com/S2klpTS
dynamical-systems kinematics
dynamical-systems kinematics
edited 2 days ago
rafa11111
956417
asked 2 days ago
Aleksić Željko
1
New contributor
Aleksić Željko is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 2 days ago
rafa11111
956417
asked 2 days ago
Aleksić Željko
1
New contributor
Aleksić Željko is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 2 days ago
rafa11111
956417
edited 2 days ago
rafa11111
956417
edited 2 days ago
rafa11111
956417
956417
asked 2 days ago
Aleksić Željko
1
New contributor
Aleksić Željko is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 days ago
Aleksić Željko
1
asked 2 days ago
Aleksić Željko
1
1
New contributor
Aleksić Željko is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Aleksić Željko is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Aleksić Željko is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
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