Mississippi steamboat on a lake #208

Peter230655 · 2024-08-20T15:11:27Z

A boat is on a lake. It has a water wheel on each side to drive and to stir it, hence the name Mississippi. The control variables are the torques applied to each wheel. The goal is to get it from A to B. the objective function is a linear combination of minimizing the energy and minimizing the time needed. the drag force on a body with speed $\bar v$ is modeled as
$F_D = -c \cdot A \cdot | \bar v |^2 \cdot \dfrac{\bar v}{| \bar v |}$, where c is the drag coefficient and A is the surface facing the flow.
I do not print the EOMs as they have around 850 operations. Else, I hope all close to examples-gallery standards.

moorepants · 2024-08-23T11:11:20Z

Error:

/home/moorepants/src/opty/docs/examples/plot_Mississippi_steamboat.rst:307: WARNING: Title underline too short.

Set up the Optimization Problem and Solve it.
--------------------------------------------
/home/moorepants/src/opty/docs/examples/plot_Mississippi_steamboat.rst:307: WARNING: Title underline too short.

Set up the Optimization Problem and Solve it.
--------------------------------------------

moorepants · 2024-08-23T11:46:03Z

examples-gallery/plot_Mississippi_steamboat.py

+# - :math:`A_S`: body fixed frame of the steamboat
+# - :math:`A_{LW}`: body fixed frame of the left wheel
+# - :math:`A_{RW}`: body fixed frame of the right wheel
+# - :math:`Dmc_S`: center of the steamboat


Is the "mc" supposed to be a subscript?

Is the "mc" supposed to be a subscript?

No, Sir. I always use, if possible Dmc to be the ceter of mass of some body. I must have copied this from some example a long time ago. If I have Dmc in a name in my code I know it is a center of mass of something.

I'm asking more because the math renders awkwardly, not because I don't like your naming conventions. You have these symbols as proper math, so I would expect them to have proper super and subscripts.

I'm asking more because the math renders awkwardly, not because I don't like your naming conventions. You have these symbols as proper math, so I would expect them to have proper super and subscripts.

If I understand you correctly, something like $Dmc_S$ looks awkward?
Would DmcS be better? (I do not want to give up Dmc)

I would expect something more like:

$$ D_{{mc}_s} $$

or

$$ D^{mc}_s $$

We typically use $A_o$ or $A^*$ for the mass center of rigid body $A$.

We typically use A o or A ∗ for the mass center of rigid body A .

I thought capital A was 'reserved' for body fixed frames?
So, I could change to $D_{S}^{mc}$ ?

You can use any letter you want for a frame, I meant that if you have a frame $X$, then the mass center is $X_o$ or $X^*$.

You can use any letter you want for a frame, I meant that if you have a frame X , then the mass center is X o or X ∗ .

So, if the body fixed frame of my steamboat is $A_S$, then $A^o_S$ could be its mass center? This makes sense!
In the code AS would be the frame and AoS the center of gravity. Should I change the designation like this?

moorepants · 2024-08-23T11:46:40Z

examples-gallery/plot_Mississippi_steamboat.py

+# - :math:`FP_{RW}`: point where the force due to rotation of the right
+#   wheel is applied
+
+N, AS, ALW, ARW = sm.symbols('N, AS, ALW, ARW', cls = me.ReferenceFrame)


Suggested change

N, AS, ALW, ARW = sm.symbols('N, AS, ALW, ARW', cls = me.ReferenceFrame)

N, AS, ALW, ARW = sm.symbols('N, AS, ALW, ARW', cls=me.ReferenceFrame)

PEP8: no space around kwarg equals signs.

moorepants · 2024-08-23T11:50:21Z

examples-gallery/plot_Mississippi_steamboat.py

+# Set up the drag forces acting on the boat.
+#
+# The drag force acting on a body moving in a fluid is given by
+# :math:`F_D = -c \cdot A \cdot | \bar v|^2 \cdot \dfrac{\bar v}{| \bar v|}`,


Drag force is more typically:

$$ F = -\textrm{sgn}(v)\frac{1}{2} \rho C_D A v^2 $$

where $\rho$ is the density of the fluid.

In my article, which I will remove and replace, there was the 'suggestion' to lump $\rho, C_D, \frac{1}{2}$ into one variable.
Hence I did it.

moorepants · 2024-08-23T11:51:03Z

examples-gallery/plot_Mississippi_steamboat.py

+# vector of the body and :math:`A` is the cross section area of the body facing
+# the flow. This may be found here:
+#
+# https://courses.lumenlearning.com/suny-physics/chapter/5-2-drag-forces/


You can remove this link, as it is a textbook equation. Or better link to a wikipedia article about it.

You can remove this link, as it is a textbook equation. Or better link to a wikipedia article about it.

this one o.k.?
https://en.wikipedia.org/wiki/Drag_(physics)

There is a whole page about the "drag equation": https://en.wikipedia.org/wiki/Drag_equation

moorepants · 2024-08-23T11:52:32Z

examples-gallery/plot_Mississippi_steamboat.py

+# ( :math:`\circ` denotes the inner product)
+#
+# :math:`F_{D_x} = -c \cdot A \cdot (A.x \circ \bar v)^2 \cdot \operatorname{sgn}(A.x \circ \bar v) \cdot A.x`
+# :math:`F_{D_y} = -c \cdot A \cdot (A.y \circ \bar v)^2 \cdot \operatorname{sgn}(A.y \circ \bar v) \cdot A.y`


I typically use \cdot for dot product and do not use a symbol for scalar multiplication, e.g. $a\hat{b}_x\cdot\hat{a}_x$.

Also, sympy prints unit vectors like: \hat{\mathbf{a}}_x.

moorepants · 2024-08-23T11:54:51Z

examples-gallery/plot_Mississippi_steamboat.py

+# As an (infinitely often) differentiable approximation of the sign function,
+# I will use the fairly standard approximation:
+#
+# :math:`\operatorname{sgn}(x) \approx \tanh( \alpha \cdot x )` with :math:`\alpha \gg 1`


If you specify all the variables to have correct assumptions (for example real=True or nonegative=True, then you can use Abs() and it will differentiate once and print with the C printers. I don't think you have to use this tangent function.

If you specify all the variables to have correct assumptions (for example real=True or nonegative=True, then you can use Abs() and it will differentiate once and print with the C printers. I don't think you have to use this tangent function.

Mathematically abs(x-a) is not differentiable at x=a, or so I understand it. How does sympy go around this?
(I had a problem with opty and abs before, but I do not think, I declared the variables to be real)

In [1]: import sympy as sm In [2]: t = sm.symbols('t', real=True, nonnegative=True) In [3]: v = sm.Function('v', real=True)(t) In [4]: f = sm.Abs(v) In [5]: f Out[5]: Abs(v(t)) In [6]: f.diff(t) Out[6]: sign(v(t))*Derivative(v(t), t) In [7]: f.diff(v) Out[7]: sign(v(t))*Derivative(v(t), v(t))

Thanks!
This means, sympy defines $\dfrac{d}{dt} abs(x(t)) = 0$ at x(t) = 0, it seems.
Out[7] is not differentiable at v(t) = 0.
Would opty not 'prefer' functions whose derivatives are smooth, or does this not affect convergence?
(my gut feeling is that the more often the functions are differentiable the better the convergence - but my gut feeling was off before!!)

Should I try with sm.Abs(....)?
You wrote; t = sm.symbols('t', real=True, nonnegative=True)
I recall you told me it is better to use t = me.dynamicsymbols._t

Probably just leave it as the tanh function.

I recall you told me it is better to use t = me.dynamicsymbols._t

That is required if you use the default symbol for t in sympy.physics.mechanics. But you can set t to any variable you want.

examples-gallery/plot_Mississippi_steamboat.py

Peter230655 · 2024-08-23T13:23:53Z

I (hopefully) made all the corrections you suggested, except I did not dare replacing the tanh(x) expression with the equivalent abs(x) expression. opty does not 'like' functions which are not differentiable, you told me at least once before.

NB: Let me look at my other two PRs and correct what you suggested here, before you waste your time telling me the same mistakes which I made here.

moorepants · 2024-08-23T16:10:33Z

Here is a trick for using Abs() (but not required for this example). https://github.com/csu-hmc/gait2d/blob/master/pygait2d/segment.py#L444

Peter230655 · 2024-08-23T16:36:11Z

I used the link to drag force you gave.
I used $D^{mc}_X$ to designate the center of gravity of body X

Peter230655 · 2024-08-24T03:45:09Z

I renamed the mass centers as follows:
if $A_S$ is the body fixed frame of S, then its center of mass is $A^o_S$

Peter230655 · 2024-08-24T09:11:31Z

Here is a trick for using Abs() (but not required for this example). https://github.com/csu-hmc/gait2d/blob/master/pygait2d/segment.py#L444

Now I remember, clever! I believe you showed this no me in another context, it was this trick:
penetration = (abs(y_position) - y_position) / 2.
you showed to me then.

Would it be a sound rule of thumb for opty to avoid function which are not differentiable at certain points unless one is sure, these points will never be close to the optimum solution of opty?

Peter230655 · 2024-08-26T05:52:24Z

Hold off with this one, please.
I may have oversimplified the moment caused by a rotation of the steamboat.

Peter230655 · 2024-08-26T18:22:12Z

These two commits are the same, I just had some problem (I am still not very perfect with this github stuff), so I committed again.
All I changed was a more realistic formula for the torque ehrn the boat rotates.

I made some error in github!

moorepants · 2024-10-17T04:39:46Z

Thanks, merged!

Peter230655 · 2024-10-17T04:41:52Z

Thanks, merged!

Thank you! :-)
So, even proper names, like Mississippi should be lower case in the name.

moorepants · 2024-10-17T04:45:09Z

I just follow PEP8 on Python module filenames:

Modules should have short, all-lowercase names. Underscores can be used in the module name if it improves readability. Python packages should also have short, all-lowercase names, although the use of underscores is discouraged.

moorepants · 2024-10-17T04:46:18Z

https://google.github.io/styleguide/pyguide.html#3164-guidelines-derived-from-guidos-recommendations

Peter230655 · 2024-10-17T04:52:15Z

https://google.github.io/styleguide/pyguide.html#3164-guidelines-derived-from-guidos-recommendations

Clear!
So modules like this: this_is_a_module
Packages like this: this-is-a-package

moorepants · 2024-10-17T04:54:13Z

No, they all use underscores. If you name a file a-b-c.py then you can't import it import a-b-c because the - is interpreted as subtraction in python.

Peter230655 · 2024-10-17T04:58:23Z

No, they all use underscores. If you name a file a-b-c.py then you can't import it import a-b-c because the - is interpreted as subtraction in python.

so, either thisisapackage or this_is_a_package

moorepants · 2024-10-17T05:01:09Z

yes

Mississippi steamboat on a lake

b01d251

corrected the underline

b0b216c

moorepants reviewed Aug 23, 2024

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