## herclau

Mr. Hermes Rozsa Iglesias

## 1038 Reputation

19 years, 242 days

## restart;From   m[t]*(1-rho[...

restart;
From
m[t]*(1-rho[a]/rho[t]) = m[r]*(1-rho[a]/rho[r])+`&Deltaw`;

and
m[t] := m[ct]*(1-rho[0]/rho[c])/(1-rho[0]/rho[t]);

m[r] := m[cr]*(1-rho[0]/rho[c])/(1-rho[0]/rho[r]);

I need to get

m[a] = m[a]*(1+C)+`&Deltaw`;
C = (rho[a]-rho[0])*(1/rho[t]-1/rho[r]); Developing m[t]*(1-rho[a]/rho[t]) = m[r]*(1-rho[a]/rho[r])+`&Deltaw`; I got /    rho[0]\ /    rho[a]\         /    rho[0]\ /    rho[a]\
m[ct] |1 - ------| |1 - ------|   m[cr] |1 - ------| |1 - ------|
\    rho[c]/ \    rho[t]/         \    rho[c]/ \    rho[r]/
------------------------------- = ------------------------------- + &Deltaw
rho[0]                            rho[0]
1 - ------                        1 - ------
rho[t]                            rho[r]       isolate(m[ct]*(1-rho[0]/rho[c])*(1-rho[a]/rho[t])/(1-rho[0]/rho[t]) = m[cr]*(1-rho[0]/rho[c])*(1-rho[a]/rho[r])/(1-rho[0]/rho[r])+`&Delta;w`, m[ct]);
/      /    rho[0]\ /    rho[a]\           \
|m[cr] |1 - ------| |1 - ------|           |
|      \    rho[c]/ \    rho[r]/           | /    rho[0]\
|------------------------------- + &Deltaw | |1 - ------|
|              rho[0]                      | \    rho[t]/
|          1 - ------                      |
\              rho[r]                      /
m[ct] = ---------------------------------------------------------
/    rho[0]\ /    rho[a]\
|1 - ------| |1 - ------|
\    rho[c]/ \    rho[t]/    simplify(m[ct] = (m[cr]*(1-rho[0]/rho[c])*(1-rho[a]/rho[r])/(1-rho[0]/rho[r])+`&Deltaw`)*(1-rho[0]/rho[t])/((1-rho[0]/rho[c])*(1-rho[a]/rho[t])), 'symbolic');                                      1
m[ct] = - -------------------------------------------------------- ((
(-rho[r] + rho[0]) (-rho[c] + rho[0]) (-rho[t] + rho[a])
-m[cr] rho[c] rho[r] + m[cr] rho[c] rho[a] + m[cr] rho[0] rho[r]
- m[cr] rho[0] rho[a] - &Delta;w rho[c] rho[r] + &Deltaw rho[c] rho[0]) (
-rho[t] + rho[0]))
rhs(m[ct] = -(-m[cr]*rho[c]*rho[r]+m[cr]*rho[c]*rho[a]+m[cr]*rho[0]*rho[r]-m[cr]*rho[0]*rho[a]-`&Deltaw`*rho[c]*rho[r]+`&Deltaw`*rho[c]*rho[0])*(-rho[t]+rho[0])/((-rho[r]+rho[0])*(-rho[c]+rho[0])*(-rho[t]+rho[a])))
1
- -------------------------------------------------------- ((
(-rho[r] + rho[0]) (-rho[c] + rho[0]) (-rho[t] + rho[a])
-m[cr] rho[c] rho[r] + m[cr] rho[c] rho[a] + m[cr] rho[0] rho[r]
- m[cr] rho[0] rho[a] - &Delta;w rho[c] rho[r] + &Delta;w rho[c] rho[0]) (
-rho[t] + rho[0])) factor(-(-m[cr]*rho[c]*rho[r]+m[cr]*rho[c]*rho[a]+m[cr]*rho[0]*rho[r]-m[cr]*rho[0]*rho[a]-`&Deltaw`*rho[c]*rho[r]+`&Deltaw`*rho[c]*rho[0])*(-rho[t]+rho[0])/((-rho[r]+rho[0])*(-rho[c]+rho[0])*(-rho[t]+rho[a])));                             1
- -------------------------------------------------------- ((
(-rho[r] + rho[0]) (-rho[c] + rho[0]) (-rho[t] + rho[a])
-m[cr] rho[c] rho[r] + m[cr] rho[c] rho[a] + m[cr] rho[0] rho[r]
- m[cr] rho[0] rho[a] - &Deltaw rho[c] rho[r] + &Deltaw rho[c] rho[0]) (
-rho[t] + rho[0])) My attempts using other functions of maple without unsuccessful.
Any suggestions? Gracias HerClau

## phase trajectories Brief comment...

Brief comment:

that picture let us now see the impact on behavior of phase  trajectories of a conservative system of linear friction. And then if the friction is sufficiently small, ie, the possible oscillation of the pendulum about the equilibrium, then can show that the phase trajectories are such as schematically shown in Fig. If friction does not allow any of the pendulum about the situation equilibrium, the picture of the phase trajectories will be another.

we can see that the seat remained saddles (we consider only a sufficiently small neighborhood of singular points), but in the neighborhood of points (± 2Pi m, 0),where m = 0, 1,2. . Closed phase trajectories low friction shove in a spiral, and with a strong friction in the trajectory, which "includes" in the singular points in the set certain directions. In the case of spirals come to a special point of focus, in which case the singular point nazy -called a node.
The singular point of two-dimensional autonomous differential equation called the focus, if there is a neighborhood of this point,completely filled disjoint phase trajectories, trajectories similar to spirals, which are "wound" at singular point or when t -> + a  or at t ->a. which each of the phase trajectory behaves like branch of the parabola or a half-line, adjacent to the study point in a certain direction.

## trial and error...

Thank you,
In this way try to find the parameters and initial conditions to achieve

Something like a trial and error.

There are mechanism more analytical, more mathematical?

Gracias

HerClau

## DEplot with Explore...

Thanks Jakubi,
What is not clear, how to take the initial conditions to achieve the chart shown.

http://www.mapleprimes.com/files/9494_PIC%2055.jpg

How can I use the Explore to analyze the graph DEplots obtained by varying the parameters c, k and the initial conditions?

diff(x(t), t, t)+c*(diff(x(t), t))+k*sin(x(t)) = 0;

Is it possible?

Gracias

HerClau

## Thank...

Thank you very much Robert Israel, this has been of much help.

## What is the problem? Is this usual?...

Hi Doug:

Following your instructions I have made some progress:

" I'm using worksheets in the Standard interface, with 1D input. The only editing I do in MaplePrimes is to change the format from Normal to Formatted."The problem is as follows:
When I copy from Maple to MaplePrimes, the content does not paste to it.
To achieve this I had to use notepad.

What is the problem? Is this usual?
HerClau

## You could flag your own post...

How I tell the system that I want to delete a certain part of the comment? And how to label the part to remove?

HerClau

## problems with the conversion of units...

I share the worksheet, which presents problems with the conversion of units, and problems with the solve command.

Gracias
Thanks

HerClau

## Dear Colleagues: Printed...

Dear Colleagues:

Printed the suggestion, I read and print the help, guidance found in:

I tried to implement at some reviews, and can not find the most viable and easy to share and evacuate my doubts.

These 82 comments were with much work and effort, I think for you guys too.
At this time, urges me to know: how to edit or delete a comment already posted?

Impatient to their orientation, suggestions and comments.

Some pictures I saw them public as follows:

It is a configuration problem of IE? How to solve it?

Grateful and sorry for my, nothing presentable, comments.

## Solve with units...

Hello Colleagues, This is extensive. I thought it would be easier to finish.

There is way to solve this problem or do I work without units?

Gracias
HerCalu

## Help Me!!!!!...

Help Me
How to delete or edit a post that did not go as expected?
HerClau

## This post was generated using the MapleP...

 Crema de leche caf© Taza

This post was generated using the MaplePrimes File Manager

View 9494_Cafe Units2.mw on MapleNet or Download 9494_Cafe Units2.mw
View file details

## How to understand this result?...

How to understand this result? Where is the error? The Café had a temperature of 80 ° C. and environmental temperature is 20 ° C.
How he reached about 67 K?
combine(Ca(Units[Standard][`*`](2, Unit('s'))), 'units');
Units[Standard][`*`](67.69129342, Unit('K'))

convert(combine(67.69129342*Unit('K'), 'units'), 'units', degC)
Units[Standard][`*`](67.69129342, Unit('degC'))

Gracias
HerClau

## Doug Replying to: "If you...

Doug

"If you have more questions about this, maybe it would help if you could share your work as a worksheet and let some of us format it in different ways."

I share this worksheet. This is the way we usually work.

Gracias

HerClau

## Rename the file...

Rename the file. I hope you can now access it.

Gracias

HerClau

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