gibson:teaching:spring-2016:math445:lab10
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gibson:teaching:spring-2016:math445:lab10 [2016/04/12 06:39] gibson |
gibson:teaching:spring-2016:math445:lab10 [2016/04/12 06:52] (current) gibson |
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| - | **Problem 3.** Superimpose on your previous plot the path of a raindrop that falls at | + | **Problem 3.** Superimpose on your previous plot the path $\vec{x}(t)$ of a raindrop that falls at |
| - | $\vec{x} = (x,y) = (0.9,0.9)$. We're assuming the velocity of the raindrop as it drips down is proportional to the negative of the gradient of the height. That is, $\vec{v} = -c \vec{\nabla} h $, | + | $\vec{x}(0) = (x_0,y_0) = (0.9,0.9)$. We're assuming the velocity of the raindrop as it drips down is proportional to the negative of the gradient of the height. That is, $\vec{v} = -c \vec{\nabla} h $, |
| where $\vec{v} = d\vec{x}/dt$ is the $x,y$ velocity of the raindrop. For convenience set $c=1$ (this won't change the path). Then compute the path of the raindrop numerically using //forward Euler time-stepping//, | where $\vec{v} = d\vec{x}/dt$ is the $x,y$ velocity of the raindrop. For convenience set $c=1$ (this won't change the path). Then compute the path of the raindrop numerically using //forward Euler time-stepping//, | ||
gibson/teaching/spring-2016/math445/lab10.1460468362.txt.gz · Last modified: 2016/04/12 06:39 by gibson
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