The Maple help definition for spherical coordinates uses the triple (r, φ, θ) (Note the ordering!!) with φ in the range 0..Π and θ in the range 0..2Π. This means that the second entry in the triple is the zenith angle (latitude) and the third entry in th triple is the azimuth angle (longitude). This is confirmed by the relation to cartesian coordinates stated on the definition page as
x= r sin(φ) cos(θ)

y= r sin(φ) sin(θ)

z= r cos(φ)

However the help page for coords has spherical polars defined by the triple (u, v, w), with the relation to cartesian coordinates given as

x= u cos(v) sin(w)

y= u sin(v) sin(w)

z= u cos(w)

which suggests that this time it is the third entry in the triple (ie w) which is the zenith angle (latitude), with the second entry being the azimuth (longitude).

My simple-minded attempt to check which of these interpretations is correct is shown in the attached worksheet. This seems to confirm that the MapleHelp definitions page is correct and the help/coords page is incorrect - or am I missing something??

Download posVecChk.mw

Aslam-u-Alikum. Hope you will be fine. I have some error in the last command of the attached file. I want this type of answer

StressesMultiplication := Matrix(2, 2, {(1, 1) = 7, (1, 2) = 10, (2, 1) = 15, (2, 2) = 22})

n.mw

PhD (Scholar)
Department of Mathematics

f := x^2+y-z=0

f2:= y^2 +z-x = 0

after shift , solution shift too, can it be said it is invariant in parameter shift?

if not, any example to show a function which is invariant in parameter shift?

> solve(f);
/ 2 \
{ x = x, y = -x + z, z = z }
\ /
> f2 := y^2+z-x;
2
y + z - x
> solve(f2);
/ 2 \
{ x = y + z, y = y, z = z }
\ /
> f;
2
x + y - z = 0

f := x^2+y-z = 0;
originvarslist := convert(indets(f), list);
varslist := ListTools:-Rotate(convert(indets(f), list),1);
varslistm := [seq(cat(m,i),i=1..nops(varslist))];

meet difficulty in this, how to reassign to itself during the seq

f := seq(subs(originvarslist[i]=varslistm[i],f), i=1..nops(originvarslist));

f := seq(subs(varslistm[i]=varslist[i],f), i=1..nops(originvarslist));

Heaviside2.mw

I am a new user of Maple (Dec 2014).  I am trying to calculate an integral related

to mechanical loss.  Temperature is a variable in the problem (as is time), and if

I use a sinusoidal (sine or cosine) temperature-time relationship, I think all works fine.

A difficulty is that the experiments have two-hour hold times(i.e., 7200 seconds) (followed by 22 hours of sinusoidal temperature variation.)

The experiments run for several weeks or months.

I tried using Heaviside functions to model the hold times.(Constant temperature periods)

Now I am receiving errors such as " Error, (in tools/eval_foo/do) too many levels of recursion..."

Probably the Maple code is crude and/or sloppy. Most of the code is simply the setting of constants in the problem.

I will be grateful for suggestions and comments--the file is attached.  Thank you.  John B

Download Heaviside2.mwHeaviside2.mw

Hi all,

I am trying to solve the following differential equation numerically using dsolve,

y * abs (y''') = -1

y(0) =1, y'(0) = 0, y''(0)=0

it works fine when tthe absolute function is not there, i.e. yy''' = -1. 

Do you have any suggestion?

I have solved ODE's with either i.c. or b.c. (mechanics stuff) where the results were in terms of expressions, not functions.  I could plot these expressions, substitute values in for parameters, etc. 

Then I thought that the real way to solve an ODE or system of ODE's was to define functions.  I wanted this to be in three levels: the solutions in generality, the solutions with i.c./m.c. applied, and then further with the parameter values defined. 

So far, no joy.  Lots of confusion--input eqns as sequence, list, set?  I looked on the Maple help page, thought I was doing things right. I even tried out "union" for the ode's and the ic's.

The code is below; statement (11) produces an error. Yes, I am using Maple 18, even though the file says Maple 15.  I'd like to solve the 4-ODE system at the three levels listed above, and then (if possible), plot the result! Am I asking too much?  Should I be using MapleSim or some other product instead?

Thanks for any and all help!

robert w.

Download mae340_state_space_4-ode_system.mw

how to shift shift(1,[x,y,z]) = [y,z,x]

shift(2,[x,y,z]) = [z,x,y]

shift(3,[x,y,z]) = [x,y,z]

Hello Maple


I am preparing for an examination in Calculus, but my worksheet in Maple 18 doesn't cooperate. 

A lot of my studypartners use Maple 16 and they have no problems. 


I meet the following error: 

- Error, (in solve) invalid input: hastype expects 2 arguments, but received 1


I'm totally sure, that I'm typing correctly, because I write just the same as my studypartners. 
So is it an error, which only is seen in Maple 18 and can I do anything to solve the problem?

Kind regards
Anders Kristensen

PS: I can't figure out how to add a picture

I solve the problem on computational geometry: "A cube of side one contains two cubes of sides a and b having non-overlapping interiors. How to prove the inequality a+b≤1?" To this end I use the DirectSearch package , namely,

Here are some comments to it. The cube of side a is centered at (x_1,y_1,z_1) and rotated by the angles phi_1, psi_1, theta_1 (see http://uk.wikipedia.org/wiki/%D0%95%D0%B9%D0%BB%D0%B5%D1%80%D0%BE%D0%B2%D1%96_%D0%BA%D1%83%D1%82%D0%B8 ) and the cube of side b is centered at (x_2,y_2,z_2) and rotated by the angles phi_2, psi_2, theta_2. The procedure

calculates the distance between these cubes, for example,

st := time(); dist(.2, .9, .2, .2, .2, .7, .7, .7, 0, 0, 0, 0, 0, 0); time()-st;

[HFloat(5.453016092898238e-11), [s1 = HFloat(0.2646161775314957),

  s2 = HFloat(0.2828503247068887),

  s3 = HFloat(0.29444713116943216),

  t1 = HFloat(0.2646161774916062),

  t2 = HFloat(0.28285032471998384),

  t3 = HFloat(0.2944471311346344)], 2527]
                            191.133
Unfortunately, my code (which is syntactically correct) is spinning on my wondercomp during 10 hours without any output. I don't understand it at all. Your advices are welcome.

twocubes.mw

Hi there,

I have an ODE system which apparently needs some initial conditions to have its vector field plotted.

I am giving Maple's dfieldplot function the following arguments:

dfieldplot([de1, de2], [A(t), G(t)], t = 0..1, [A(0) = 25, G(0) = 0], A = 0..900, G = 0..200)

But Maple yields an error that reads:

Error, (in DEtools%2Fdfieldplot) invalid use of initial points or option - see phaseportrait

I would say that the initial conditions are correctly stated, according to the documentation of the function.

This is the attempt: MaplePrimes_Malaria_infection_cont.mw

Any ideas on what's missing?

Thanks,

jon

Hi there,

I would like to have the Jacobian matrix of an ODE system evaluated, and their eigenvalues computed, at the steady states of the system.

I know how to get the Jacobian matrix evaluated and the eigenvalues computed on an individual basis, setting manually each steady state as the argument of the matrix.

However, I would like to have it in a loop, so that the loop manages all steady states, that is:

steadyStates:= solve(mySystem); # would yield a set of pairs/lists

for each steadyState

m:=Jacobian(steadyStateN); # evaluate the Jacobian matrix

ev:= eigenvals(m); # compute the eigenvalues and save them to another variable/array and print them

end for:

First, I am not to find a way to loop over my steadyStates.

Attached is an example where the Jacobian matrix and eigenvalues are computed individually, where the steady states have been hard-coded once they have been computed: MaplePrimes_Predator_prey_model_Jacobian.mw

Any ideas on how to do this?

Thanks,

jon

Hi there,

I would like to compute and display the nullclines of a set of ordinary differential equations.

AFAIK, I can compute the nullclines in Maple by defining the equations and solving the system

e.g.:

# Define the equations
eq1 := u(t)*(1-u(t)/kappa)-u(t)*v(t) = 0;
eq2 := g*(u(t)-1)*v(t) = 0;

# Solve the system (i.e. compute the nullclines)
sol := solve({eq1, eq2}, {u(t), v(t)});

However, I am not quite able to imagine how to display them over a dfieldplot or a phaseportrait.

Attached is an example with some differential equations, and their vector field and trajectories: MaplePrimes_Predator_prey_model_nullclines.mw.

It can be use to illustrate how to (compute and) display the nullclines.

Thank you,

jon

Hi there,

I would like to have an operator (in this case, the natural logarithm) applied to a list/array of points defined as:

ydata := [0.572594976618e-1, 0.327865007249e-1, 0.280821589546e-1, 0.114365745192e-1, 0.578537931608e-2, 0.139154661062e-2, 0.641467839994e-3, 0.18013801847e-3];

How can I apply Maple's ln() operator to the whole array (i.e. avoid to apply it to ydata [1], ydata [2], etc.)?

Thank you,

jon

Aslam-u-Alikum. Hope you will be fine. I facing the problem of the last line to the attached program. I need the values of lambda in decimal.

Help.mw

PhD (Scholar)
Department of Mathematics