Odesolve and a boundary problem (Mathcad Prime)

[ValeryOchkov]

No complete happiness in life

The odesolve function of Mathcad 15 cannot work with units but can work with a boundary problem.

The odesolve function of Mathcad Prime can work with units but cannot work with a boundary problem.

Or I do someone wrong in Mathcad Prime?

See the attach and the picture:

Mathcad 15:

Prime:

[AlanStevens · Accepted solution]

Although it's annoying that Prime doesn't do the boundary condition case as simply as M15, it's actually not all that difficult to add a simple extra solve block to find the initial velocity that produces the desired end condition - see attached. This is also much simpler (to my mind, anyway) than using sbval.

Alan

PS I agree though, that Prime should be able to do it as simply as M15.

PPS Apologies for using state-space approach again - I just find it easier to think about that way!

[ValeryOchkov]

Thanks. Alan!

AlanStevens wrote:

PPS Apologies for using state-space approach again - I just find it easier to think about that way!

I'm ashamed to say I thought you went to the spree - was celebrated in English pubs the title of Hero of the Month

[ValeryOchkov]

AlanStevens wrote:

Although it's annoying that Prime doesn't do the boundary condition case as simply as M15, it's actually not all that difficult to add a simple extra solve block to find the initial velocity that produces the desired end condition - see attached. This is also much simpler (to my mind, anyway) than using sbval.

Yes!

And see please my solution. Try input in attach tend=100 s

[AlanStevens]

Valery Ochkov wrote:

And see please my solution. Try input in attach tend=100 s

Hmm! With tend = 100s the initial velocity not only exceeds Earth's escape velocity, but is also way faster than the speed of light!

It shows that the root function performs better than the solve block here though (the root function also works in my worksheet).

Alan

[ValeryOchkov]

AlanStevens wrote:

Valery Ochkov wrote:

And see please my solution. Try input in attach tend=100 s

Hmm! With tend = 100s the initial velocity not only exceeds Earth's escape velocity, but is also way faster than the speed of light!

Alan

I always keep telling my students that we need to use wisely not only nature, but also the mathematical models.

In this connection, I have a new ode problem - an iron meteorite (the ball with a known diameter, heat capacity and melting temperature) flies from space to earth. At what height meteorite melted. The k factor is known and we know - 10% of friction energy goes into the air, and another - to the meteor.

Ro air and g are functions of h.

широта - geographic latitude.

Ro(h) see - http://communities.ptc.com/message/188062

[AlanStevens]

Valery Ochkov wrote:

In this connection, I have a new ode problem - an iron meteorite (the ball with a known diameter, heat capacity and melting temperature) flies from space to earth. At what height meteorite melted. The k factor is known and we know - 10% of friction energy goes into the air, and another - to the meteor.

Ro air and g are functions of h.

Ok, here's a very simple model.

Alan

Attachment corrected.

[ValeryOchkov]

Thanks, Alan!

The solution is fine. I have added one plot. Now we an/must think about Re, Pr, Bio etc

PS

1812 - the year when Napoleon burned Moscow and the beginning the "sunset" of Napoleon - the brightest "meteor" of the 19th century.

[ValeryOchkov]

Another dirty trick of Mathcad Prime - we cannot reverse axes scale of plots:

Mathcad 15

Mathcad Prime:

[ViktorKorobov]

As for the problem of a large meteorite on display.
More correct wording, in my opinion, should be - at what height begin meteorite melts (or reached the temperature of melting). The fact that the complete melting also take some time associated with the specific heat of fusion of iron, the value of which is not specified in the statement.
In addition, the subject must be told that we neglect the reaction of oxidation of iron (which, at temperatures close to the melting point, is the place to be to a large extent, I think).

Viktor

[ValeryOchkov]

AlanStevens wrote:

Hmm! With tend = 100s the initial velocity not only exceeds Earth's escape velocity, but is also way faster than the speed of light!

Alan

[ValeryOchkov]

I have a dream to write (cowrite) a book

A.Stevens and V.Ochkov (or V.Ochkov and A.Stevens or V.Ochkov, A.Stevens and PTC) "Book of problems in physics with Mathcad (and Maple)"

Like this

http://www.springer.com/chemistry/physical+chemistry/book/978-3-7091-0530-6

and

this

http://www.springer.com/engineering/computational+intelligence+and+complexity/book/978-3-540-20852-5

Springer is ready to publish it!

[AlanStevens]

Valery Ochkov wrote:

I have a dream to write (cowrite) a book

A.Stevens and V.Ochkov (or V.Ochkov and A.Stevens or V.Ochkov, A.Stevens and PTC) "Book of problems in physics with Mathcad (and Maple)"

Springer is ready to publish it!

That would be fine, but we'd need more than just a few ball trajectory problems!

Alan

[ValeryOchkov]

AlanStevens wrote:

Valery Ochkov wrote:

I have a dream to write (cowrite) a book

A.Stevens and V.Ochkov (or V.Ochkov and A.Stevens or V.Ochkov, A.Stevens and PTC) "Book of problems in physics with Mathcad (and Maple)"

Springer is ready to publish it!

That would be fine, but we'd need more than just a few ball trajectory problems!

Alan

No problem.

Rather, the problem is. I have many problems in thermodynamics. What sections of physics still is:
Section of mechanics
Thermodynamics
Sections electrodynamics
Oscillations and Waves
Sections statistical physics
Sections of quantum physics
Sections of particle physics
Sections of Atomic Physics
Sections of Nuclear Physics
Sections of Chemical Physics
The field theory

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