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plot a 2D arc in a coordicates which is in 3D coor...

Asked by: simonzh 0
homework
May 13 2015
0  1

In a local coordivates frame {B}, an arc whith center "coc" ,radius "radius" and angle between “alpha1” and “alpha2” can be plotted in XY plane of {B}. The coord {B} is in a Ref frame {O}. The homogeneous transformation matrix is “H”. How can I plot this arc in coordinate {O}？

Solve equations...

Asked by: yangtheary 215
solve
May 13 2015
1  7

solve 30a+75b+110c+85d+255e+160f+15g+12h+120i=800000 over the positive integers

general case of floats not handled...

Asked by: mcyf0913 5
groebner basis float
May 13 2015
1  1

g:=Groebner:-Basis([a-2.0*b,b-2], plex);

Groebner:-Reduce(a, g, plex); 

Error, (in content/polynom) general case of floats not handled

How to solve this problem simply？

complicated wave equation ...

Asked by: mostibra 20
pde wave
May 12 2015
0  1

now the equation is

d2u/dt2-(2*d2u/x2)+d2u/dxdt=0    

initial condition: u(x,0)=1-(xsign(x)), abslute x<1,0 otherwise. Assume sign(x)=-1 for x<0, 1for x>0 

 Ut(x,0)=cos(pix), bslute x<1, 0 otherwise , he didnt give any B.Cs

so I would like to know the analytical and numerical sols, and plots for the wave at t=2,4

for Numerical:   delta x=0.1, delta t=0.025, range 0..4

How can error convergence be corrected?...

Asked by: emmantop 40
numeric bvp
May 12 2015
0  9

Good day,

How can this be corrected ''Error, (in dsolve/numeric/bvp) initial Newton iteration is not converging'' see the worksheet here VT.mw

from a procedure to sub_procedure?????? how can I ...

Asked by: ben maths 20
procedure programming
May 10 2015
0  11

Hi all,
can you help in that please?
How can I use this small procedure (root_of_cheb) as a sub-procedure in  the next procedure (EvalInt) ?
is it possible?

restart:
root_of_cheb:=proc(n)
   local xk,b,k:
   xk:=(k,n)->cos((2*k-1)*Pi/(2*n));
   sort([seq(evalf(xk(k,n)),k=1..n)]):
end:
EvalInt:=proc(f,n)
   local xk:
   xk:=(k,n)->cos((2*k-1)*Pi/(2*n));
   evalf((Pi/n)*add(f(xk(i,n)),i=1..n)):
end:

Thank you

Hfloat error in solving partial differential equat...

Asked by: mobiusinfi 40
pdsolve
May 10 2015
1  7

with(PDEtools);
Es := 0.117108e12;
Ef := 0.78125e11;
l := 0.150e-6;
s := 0.500000e-3;
f := 0.5898334197e-6;
o := 0.9e-5;
d := 0.10e-17;
cb := 0.1e7/(19.9);
R := 8.3144621;
T := 298;





PDE := diff(u(x, t), t)-(diff(u(x, t)+o^2*Es*cb*u(x, t)^2/(9*R*T), x, x)) = 0;
IBC := {u(1, t) = 1, u(x, 0) = 0, (D[1](u))(1, t) = l*f/(d*cb)};
S := pdsolve(PDE, IBC, numeric, time = t, range = 0 .. 1, timestep = 0.1e-4, spacestep = 0.1e-6);
p1 := S:-plot(t = .1, numpoints = 100);
Error, (in pdsolve/numeric/plot) unable to compute solution for t>HFloat(0.0):
matrix is singular
p2 := S:-plot(t = .2, numpoints = 50, color = green);
Error, (in pdsolve/numeric/plot) unable to compute solution for t>HFloat(0.0):
matrix is singular
p3 := S:-plot(t = .3, numpoints = 50, color = blue);
Error, (in pdsolve/numeric/plot) unable to compute solution for t>HFloat(0.0):
matrix is singular
plots[display]({p1, p2, p3});
Error, (in plots:-display) expecting plot structures but received: {p1, p2, p3}


Is there a way to increase Maple's hard limits, or...

Asked by: spark1631 60
stacklimit
May 07 2015
0  3

I want to increase the stack limit. but i can not raise it above the hard limit....

 

so i wonder whether there is a way to increase the hard limit, or at least tell me how much is it?

Is there some kind of result length limit if calli...

Asked by: spark1631 60
May 07 2015
0  2

I tried to use java to call maple command, but end up jvm crash. after some digging, i found the command i issued returned a rather huge string (around 40KB...).

 

Is this the reason why jvm crash? should i constrant the length of a command result when calling it from Java code?

How to use Verlet algorithm to derive the orbit of...

Asked by: physics0150 0
homework dynamics stationary
May 06 2015
0  0

Derive the orbit of the Moon around the Earth by doing a Verlet algorith of Molecular Dynamics simulation. Use one hour for your step τ. Place the stationary Earth at the origin of the Cartesian system. For initial conditions, use the position and the speed of the Moon when it is at its apogee (furthest from Earth). Plot the orbit.

How to solve Cauchy sequences...

Asked by: laporte bernard 45
seq homework cauchy
May 05 2015
0  2

(a) Show that if {an} ∞ n=1 is Cauchy then {a 2 n} ∞ n=1 is also Cauchy. (b) Give an example of a Cauchy sequence {a 2 n} ∞ n=1 such that {an} ∞ n=1 is not Cauchy

Error, (in dsolve/numeric/process_input) unknown y...

Asked by: Mokusko 10
ode differential-equation dsolve
May 04 2015
1  5

Hi, I'm trying to solve a system of equation and I keep getting this error. Could anyone help me figure out what I'm doing wrong?

My problem is:

> alpha := .3; G := 3.5; L := 6; f := 1.1;

for i to 50 do

I0 := x(z)+y[i](z); ICon := x(0) = 1, y[i](0) = 0;

for j to 50 do

i <> j;

d1 := diff(x(z), z) = -G*x(z)*y[i](z)/IC-alpha*x(z);

d2 := diff(y[i](z), z) = G*y[i](z)*y[j](z)/IC-alpha*y[i](z);

dsys := {d1, d2};

F := dsolve({ICon, op(dsys)}, [x(z), y[i](z)], numeric);

end do;

end do;
Error, (in dsolve/numeric/process_input) unknown y[2] present in ODE system is not a specified dependent variable or evaluatable procedure


 

Open maple worksheet...

Asked by: Annonymouse 160
worksheet incomplete-question
May 04 2015
0  0

I am running Maple in a windows virtual machine, on a mac computer.

I have a number of worksheets on its disk

Windows advised me to run its error checking utility (chkdsk)

when I try and open them it gives me a number of options:

maple text

plain text 

and maple input

 

None of these are the same as the original files. What has happened? and how can i fix it?



Length of output exceed limit 1000000...

Asked by: Sofey 10
output
May 03 2015
0  3

can anybody help me? i want to check the consistency of my scheme. My equation is too long if i check manually, so i used maple 13 to simplify my equation. But it cannot simplify it because of length of output exceed limit 1000000

restart

eqn1 := u+(1-exp(-m))*u[t]+(1-exp(-m))^2*u[tt]/factorial(2)+(u-(1-exp(-m))*u[t]+(1-exp(-m))^2*u[tt]/factorial(2))-u-(1-exp(-m))*u[x]-(1-exp(-m))^2*u[xx]/factorial(2)-u+(1-exp(-m))*u[x]-(1-exp(-m))^2*u[xx]/factorial(2)+(1-exp(-m))^2*u+(1-exp(-m))^2*u^3-(1-exp(-m))^2*(4*(((x+1-exp(-m))^2-2)*cosh(x+1-exp(-m)+(t+1-exp(-m)))-(4*(x+1-exp(-m)))*sinh(x+1-exp(-m)+(t+1-exp(-m)))+(x+1-exp(-m))^6*cosh(x+1-exp(-m)+(t+1-exp(-m)))^3))*((x^2-2)*cosh(x+t)-4*x*sinh(x+t)+x^6*cosh(x+t)^3)*(((x+1-exp(-m))^2-2)*cosh(x+1-exp(-m)+t)-(4*(x+1-exp(-m)))*sinh(x+1-exp(-m)+t)+x^6*cosh(x+1-exp(-m)+t)^3)*((x^2-2)*cosh(x+1-exp(-m)+t)-4*x*sinh(x+1-exp(-m)+t)+x^6*cosh(x+1-exp(-m)+t)^3)/((((x+1-exp(-m))^2-2)*cosh(x+1-exp(-m)+(t+1-exp(-m)))-(4*(x+1-exp(-m)))*sinh(x+1-exp(-m)+(t+1-exp(-m)))+(x+1-exp(-m))^6*cosh(x+1-exp(-m)+(t+1-exp(-m)))^3)*((x^2-2)*cosh(x+t)-4*x*sinh(x+t)+x^6*cosh(x+t)^3)*(((x+1-exp(-m))^2-2)*cosh(x+1-exp(-m)+t)-(4*(x+1-exp(-m)))*sinh(x+1-exp(-m)+t)+(x+1-exp(-m))^6*cosh(x+1-exp(-m)+t)^3+(x^2-2)*cosh(x+1-exp(-m)+t)-4*x*sinh(x+1-exp(-m)+t)+x^6*cosh(x+1-exp(-m)+t)^3)+(((x+1-exp(-m))^2-2)*cosh(x+1-exp(-m)+t)-(4*(x+1-exp(-m)))*sinh(x+1-exp(-m)+t)+(x+1-exp(-m))^6*cosh(x+1-exp(-m)+t)^3)*((x^2-2)*cosh(x+1-exp(-m)+t)-4*x*sinh(x+1-exp(-m)+t)+x^6*cosh(x+1-exp(-m)+t)^3)*(((x+1-exp(-m))^2-2)*cosh(x+1-exp(-m)+(t+1-exp(-m)))-(4*(x+1-exp(-m)))*sinh(x+1-exp(-m)+(t+1-exp(-m)))+(x+1-exp(-m))^6*cosh(x+1-exp(-m)+(t+1-exp(-m)))^3+(x^2-2)*cosh(x+t)-4*x*sinh(x+t)+x^6*cosh(x+t)^3));

(1-exp(-m))^2*u[tt]-(1-exp(-m))^2*u[xx]+(1-exp(-m))^2*u+(1-exp(-m))^2*u^3-(1-exp(-m))^2*(4*((x+1-exp(-m))^2-2)*cosh(x+2-2*exp(-m)+t)-16*(x+1-exp(-m))*sinh(x+2-2*exp(-m)+t)+4*(x+1-exp(-m))^6*cosh(x+2-2*exp(-m)+t)^3)*((x^2-2)*cosh(x+t)-4*x*sinh(x+t)+x^6*cosh(x+t)^3)*(((x+1-exp(-m))^2-2)*cosh(x+1-exp(-m)+t)-4*(x+1-exp(-m))*sinh(x+1-exp(-m)+t)+x^6*cosh(x+1-exp(-m)+t)^3)*((x^2-2)*cosh(x+1-exp(-m)+t)-4*x*sinh(x+1-exp(-m)+t)+x^6*cosh(x+1-exp(-m)+t)^3)/((((x+1-exp(-m))^2-2)*cosh(x+2-2*exp(-m)+t)-4*(x+1-exp(-m))*sinh(x+2-2*exp(-m)+t)+(x+1-exp(-m))^6*cosh(x+2-2*exp(-m)+t)^3)*((x^2-2)*cosh(x+t)-4*x*sinh(x+t)+x^6*cosh(x+t)^3)*(((x+1-exp(-m))^2-2)*cosh(x+1-exp(-m)+t)-4*(x+1-exp(-m))*sinh(x+1-exp(-m)+t)+(x+1-exp(-m))^6*cosh(x+1-exp(-m)+t)^3+(x^2-2)*cosh(x+1-exp(-m)+t)-4*x*sinh(x+1-exp(-m)+t)+x^6*cosh(x+1-exp(-m)+t)^3)+(((x+1-exp(-m))^2-2)*cosh(x+1-exp(-m)+t)-4*(x+1-exp(-m))*sinh(x+1-exp(-m)+t)+(x+1-exp(-m))^6*cosh(x+1-exp(-m)+t)^3)*((x^2-2)*cosh(x+1-exp(-m)+t)-4*x*sinh(x+1-exp(-m)+t)+x^6*cosh(x+1-exp(-m)+t)^3)*(((x+1-exp(-m))^2-2)*cosh(x+2-2*exp(-m)+t)-4*(x+1-exp(-m))*sinh(x+2-2*exp(-m)+t)+(x+1-exp(-m))^6*cosh(x+2-2*exp(-m)+t)^3+(x^2-2)*cosh(x+t)-4*x*sinh(x+t)+x^6*cosh(x+t)^3))

 (1)

a := simplify(eqn1);

`[Length of output exceeds limit of 1000000]`

 (2)

``


Download consistency_expmle_4.mw

.

how to prove with maple...

Asked by: laporte bernard 45
student
May 03 2015
0  1


> 

"the set Q of rational numbers does not have the least-upper-bound property under the usual order. "
> 

Proof:
> 

"Consider the part A = {x in `&Qopf;`; 1<x^(2)<2<}, this part is not empty as [4/(3)] in A; It is bounded by 2 as if x^(2)<4 then x<2. THe set of greatest elements of A, belonging to `&Qopf;`, is not empty."
> 

Lemma:
> 

"If [p/(q)] in A with q in `&Nopf;`^(*), then p>q for p>0 and p^(2)-2*q^(2)<0; or p^(2)-2*q^(2) in `&Zopf;`, thus"
> 

p^2-2*q^2 <= -1

p^2-2*q^2 <= -1

 (1)
> 

"for all r in `&Nopf;`^(*), put y=(r*p+1)/(r.p), we have :"
> 

y > p/q
> 

Now:
> 

"y^(2)-2=supA/(r^(2)*q^(2)), with supA= r^(2)*p^(2)+2 r*p+1-2 r^(2)q^(2),"
> 

otherwise; -1; s = r(p^2-2*q^2)+2*p+1

s = r(p^2-2*q^2)+2*p+1

 (2)
> 

"a good choice for r, for instance r=2*p+1, we get from (1)"
> 

(2*p+1)(p^2-2*q^2) <= (2*p+1)(-1)

2*p(p^2-2*q^2) <= 2*p(-1)

 (3)
> 

thus:
> 

(2*p+1)(p^2-2*q^2)+2*p <= -1

2*p(p^2-2*q^2)+2*p <= -2

 (4)
> 

(2*p+1)*[(2*p+1)(p^2-2*q^2)+2*p] <= -2*p-1

(2*p+1)*[2*p(p^2-2*q^2)+1+2*p] <= -2*p-1

 (5)
> 

(2*p+1)*[(2*p+1)(p^2-2*q^2)+2*p]+1 <= -2*p

(2*p+1)*[2*p(p^2-2*q^2)+1+2*p]+1 <= -2*p

 (6)
> 

"finally, supA<0"
> 

`and`(thus*y^2 < 2, `in`(y, A*with*y^2) and A*with*y^2 > 1)
> 

"so, for any x in p/(q) in A, there exists y in A such that y>x: in conclusion A does'nt admit a greatest element."
> 

Now, given*m = p/q, `and`(not `in`(Typesetting:-delayDotProduct(a*greatest*element*of*A, Then)*m, A), we*get*thus):
> 

`and`(p > q, p^2-2*q^2 >= 0)
> 

as*the*equation*p^2-2*q^2 = (0*has)*no*solutions and `in`((0*has)*no*solutions, nonnegint*nonnegint), we*get:
> 

2*p^2-2*q^2 >= 1:
> 

"for any r in `&Nopf;`^(*)let's put m'=(r*p)/((r*q+1)); we have:"
> 

(diff(m(x), x))^2-2 = supA/(r*q+1)^2:
> 

With*supA = r^2*p^2-2*(r*q+1)^2 and r^2*p^2-2*(r*q+1)^2 = r[r[p^2-2*q^2]-4*q]-2:
> 

"for a good choice of r, for example r=4*q+1, we get (back to (2)):"
> 

supA > (0*thus)*(diff(m(x), x))^2 and (0*thus)*(diff(m(x), x))^2 > 2:
> 

"So, for any greatest element m of A, it exists m', greatest element of A such as:"
> 

diff(m(x), x) < m(x):
> 

"A does not admit a least upper bound."
> 

``


Download rational_numbers.mw

> 

"the set Q of rational numbers does not have the least-upper-bound property under the usual order. "
> 

Proof:
> 

"Consider the part A = {x in `&Qopf;`; 1<x^(2)<2<}, this part is not empty as [4/(3)] in A; It is bounded by 2 as if x^(2)<4 then x<2. THe set of greatest elements of A, belonging to `&Qopf;`, is not empty."
> 

Lemma:
> 

"If [p/(q)] in A with q in `&Nopf;`^(*), then p>q for p>0 and p^(2)-2*q^(2)<0; or p^(2)-2*q^(2) in `&Zopf;`, thus"
> 

p^2-2*q^2 <= -1

p^2-2*q^2 <= -1

 (1)
> 

"for all r in `&Nopf;`^(*), put y=(r*p+1)/(r.p), we have :"
> 

y > p/q
> 

Now:
> 

"y^(2)-2=supA/(r^(2)*q^(2)), with supA= r^(2)*p^(2)+2 r*p+1-2 r^(2)q^(2),"
> 

otherwise; -1; s = r(p^2-2*q^2)+2*p+1

s = r(p^2-2*q^2)+2*p+1

 (2)
> 

"a good choice for r, for instance r=2*p+1, we get from (1)"
> 

(2*p+1)(p^2-2*q^2) <= (2*p+1)(-1)

2*p(p^2-2*q^2) <= 2*p(-1)

 (3)
> 

thus:
> 

(2*p+1)(p^2-2*q^2)+2*p <= -1

2*p(p^2-2*q^2)+2*p <= -2

 (4)
> 

(2*p+1)*[(2*p+1)(p^2-2*q^2)+2*p] <= -2*p-1

(2*p+1)*[2*p(p^2-2*q^2)+1+2*p] <= -2*p-1

 (5)
> 

(2*p+1)*[(2*p+1)(p^2-2*q^2)+2*p]+1 <= -2*p

(2*p+1)*[2*p(p^2-2*q^2)+1+2*p]+1 <= -2*p

 (6)
> 

"finally, supA<0"
> 

`and`(thus*y^2 < 2, `in`(y, A*with*y^2) and A*with*y^2 > 1)
> 

"so, for any x in p/(q) in A, there exists y in A such that y>x: in conclusion A does'nt admit a greatest element."
> 

Now, given*m = p/q, `and`(not `in`(Typesetting:-delayDotProduct(a*greatest*element*of*A, Then)*m, A), we*get*thus):
> 

`and`(p > q, p^2-2*q^2 >= 0)
> 

as*the*equation*p^2-2*q^2 = (0*has)*no*solutions and `in`((0*has)*no*solutions, nonnegint*nonnegint), we*get:
> 

2*p^2-2*q^2 >= 1:
> 

"for any r in `&Nopf;`^(*)let's put m'=(r*p)/((r*q+1)); we have:"
> 

(diff(m(x), x))^2-2 = supA/(r*q+1)^2:
> 

With*supA = r^2*p^2-2*(r*q+1)^2 and r^2*p^2-2*(r*q+1)^2 = r[r[p^2-2*q^2]-4*q]-2:
> 

"for a good choice of r, for example r=4*q+1, we get (back to (2)):"
> 

supA > (0*thus)*(diff(m(x), x))^2 and (0*thus)*(diff(m(x), x))^2 > 2:
> 

"So, for any greatest element m of A, it exists m', greatest element of A such as:"
> 

diff(m(x), x) < m(x):
> 

"A does not admit a least upper bound."
> 

``


Download rational_numbers.mw

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