I'd like to plot the following inequalities:

sqrt(x)<=1/sqrt(2)

1/sqrt(2)<sqrt(x)<=1/sqrt(2)

> restart;
> with(plots);
> Eq1 := diff(f(eta), eta, eta, eta)+f(eta)*(diff(f(eta), eta, eta))-2*(diff(f(eta), eta))^2-M^2*(diff(f(eta), eta)) = 0;
/ d / d / d \\\ / d / d \\
|----- |----- |----- f(eta)||| + f(eta) |----- |----- f(eta)||
\ deta \ deta \ deta /// \ deta \ deta //

2
/ d \ 2 / d \
- 2 |----- f(eta)| - M |----- f(eta)| = 0
\ deta / \ deta /
> Eq2 := 1+(4/3)*R*(diff(theta(eta), eta, eta))+Pr*(f(eta)*(diff(theta(eta), eta))-(diff(f(eta), eta))*theta(eta)) = 0;
4 / d / d \\
1 + - R |----- |----- theta(eta)||
3 \ deta \ deta //

/ / d \ / d \ \
+ Pr |f(eta) |----- theta(eta)| - |----- f(eta)| theta(eta)| = 0
\ \ deta / \ deta / /
> bcs1 := f(0) = S, (D(f))(0) = 1+L*G, (D(D(f)))(0) = .1, f(6) = 0;
f(0) = S, D(f)(0) = 1 + L G, @@(D, 2)(f)(0) = 0.1, f(6) = 0
> fixedparameter := [S = .1, M = .1];
[S = 0.1, M = 0.1]
> Eq3 := eval(Eq1, fixedparameter);
/ d / d / d \\\ / d / d \\
|----- |----- |----- f(eta)||| + f(eta) |----- |----- f(eta)||
\ deta \ deta \ deta /// \ deta \ deta //

2
/ d \ / d \
- 2 |----- f(eta)| - 0.01 |----- f(eta)| = 0
\ deta / \ deta /
> fixedparameter := [R = .1, Pr = .7];
[R = 0.1, Pr = 0.7]
> Eq4 := eval(Eq2, fixedparameter);
/ d / d \\ / d \
1 + 0.1333333333 |----- |----- theta(eta)|| + 0.7 f(eta) |----- theta(eta)|
\ deta \ deta // \ deta /

/ d \
- 0.7 |----- f(eta)| theta(eta) = 0
\ deta /
> bcs2 := theta(0) = 1+T*B, (D(theta))(6) = B, theta(6) = 0;
theta(0) = 1 + T B, D(theta)(6) = B, theta(6) = 0

> T := .1; B := .1;
0.1
0.1
> L := [0., .1, .2, .3];
[0., 0.1, 0.2, 0.3]
> for k to 4 do R := dsolve(eval({Eq3, Eq4, bcs1, bcs2}, L = L[k]), [f(eta), theta(eta)], numeric, output = listprocedure); Y || k := rhs(R[2]); YL || k := rhs(R[3]) end do;
Error, (in dsolve/numeric/bvp/convertsys) too many boundary conditions: expected 6, got 7
> plot([YL || (1 .. 4)], 0 .. 6, 1 .. -.2, labels = [eta, diff(f(eta), eta)]);

A major-league pitcher releases a ball at a point 6 feet above the ground and 58 feet from home plate at a speed of 100 mi/hr ,  

If gravity had no effect, the ball would travel along a line and cross home plate 4 feet off the ground. Find the drop D caused by gravity.                                                                                                                                                      

NB: in this problem the angle alpha is the angle between the horizontal and the direction of the released ball. Since the ball is dropping, alpha will be negative.

I got a problem with a difficult ode,the commands are below.

restart;
sys := 1.*(diff(x(t), t, t)) = piecewise(b(t) = 1, 0, 1003.0-1000.*x(t)-30.*(diff(x(t), t))-25.*signum(diff(x(t), t)-.1)-.3*signum(diff(x(t), t))*exp(-2*abs(diff(x(t), t)))), x(0) = 1, (D(x))(0) = 0;
mu := 100;
stick := [diff(x(t), t) = .1, b(t) = piecewise((1000.-1000.*x(t))^2 < 10000, 1, 0)];
slip := [[0, 10000 < (1000.-1000.*x(t))^2], b(t) = 0];
sol:=dsolve({sys,b(0)=0},numeric,discrete_variables=[b(t)::float],events=[stick,slip],event_maxiter=1000000,output=listprocedure,maxfun=0,range=0..8);

any advice is appreciated.

How can I solve raychaudhuri equations numerically using GRtensor?

I want to use Maple (dsolve command) to solve this problem, how do I input the command? Part (a) is enought.

I have tried the command, but Maple says "Warning, for {u(t)} arbitrary the system is inconsistent".

Thank you very much for your help.

Further tags : implicit form, Matlab codegen for GPOPS purposes

Hi there,

I would like to introduce my self and ask you for an advice. 

I have a four linked robot that i would really like to control by the meaning of the optimal control theory. The arm has 4 actuators (giving torques U) in corrispondence of 4 rotational joints. P parameters describe the system.

I got ht edynamic system with the Lagrangian method and now I have 4 2nd order...

I'm using Maple to come up with equations, and then I'm substituting in variable names for functions which I can then output to Matlab.

I haven't had any problems until I ran into partial derivates described by the D[] operator.  For example, if i have a function f described by f(x(t),y(t)) and I differentiate it wrt t, I get 

D[1](f)(x(t),y(t))*(x(t)_dot) + D[2](f)(x(t),y(t))*(y(t)_dot)

I want to make a substitution for D[1](f)(x(t),y(t)) and D[2...

I sometimes like to work with worksheets in classic mode. However, I have just discovered that I cannot simply type "restart;" in the beginning of a worksheet in classic mode because it causes the worksheet window to freeze. However, if I click the "restart" button, then things go as normal. I really want to have each of my worksheets begin with the "restart;"  command. Need your assistant on a way out.

I use 64-bit windows 7 CORE i3 Dell Inspiron N4050.

Attached are results I obtained in MAPLE 12.  Can anyone explain the contradiction?

In short, if I sum from n = 0 to some integer I get a FALSE when testing the equality, which is what I would EXPECT.  However, if I change the integer to a variable to represent that integer such as m--> the result is TRUE?

Note the change in the variable of beta to alpha inside the series expression within the parentheses.

regards