Consider the problem of a hard-hit baseball. The air-friction drag on a baseball is approximately given by the following formula

and subsequent differential equations : 

F:=-((C_d)*rho*Pi*(r)^2*v*v)/2;
m:=0.145;
v0:=65;
g:=9.81;
v_x:=diff(x(t),t);
v_y:=diff(y(t),t);
d2v_x:=-((C_d)*rho*Pi*(r^2)*(v_x)*sqrt((v_x)^2 +(v_y)^2))/(2*m);
d2v_y:=-((C_d)*rho*Pi*(r^2)*(v_y)*sqrt((v_x)^2 +(v_y)^2))/(2*m)-g;

where

C[d] is the drag coefficient (about 0.35 for a baseball)

•
rho[air] is the density of air (about 1.2 kg/
3m
)
•
r is the radius of the ball (about 0.037 m)

v is the vector velocity of the ball

Then if given that : 

Power hitters in baseball say they would much rather play in Coors Field in Denver than in sea-level stadiums because it is so much easier to hit home runs. The air pressure in Denver is about 10% lower than it is at sea level. The field dimensions at Coors Field are:

Left Field - 347 feet (106 m)
Left-Center - 390 feet (119 m)
Center Field - 415 feet (126 m)
Right-Center - 375 feet (114 m)
Right Field - 350 feet (107 m)

 1. Overlay two plots: one at sea level and one in Denver to show why power hitters prefer Coors field.

2. Find the initial magnitude of velocity, v0

needed to hit a home run to Right-Center, where v_x(0)=v0/sqrt(2) and v_y(0)=v0/sqrt(2)

I don't quite understand how to use the field dimensions for both 1 and 2 and am pretty clueless as to how to approach this question using the ordinary differential equations mentioned above.

Hey guys, I'm new to the forum, so please tell if I need to set up the question in a different way :) I've tried to find an answer for this, but have struggled since our learning book is in danish, so the used terms may not be technically correct,

Anyways, how do you solve this problem in maple? 

Find the complete real solution for the differential equation system:

For the homogenous part I've found. (Is this correct?)

  , c1,c2 € R

I've tried to find an answer for the inhomogenous part but I get a really complicated result, so I doubt it's correct.

Thanks for the help :)

-Alex 

Is it possible to solve DDE with dsolve?

restart:

Eq1 := diff(x(t), t) = 1-.1*x(t)-0.5e-3*x(t)*v(t)/(1+0.1e-5*v(t));

Eq2 := diff(y(t), t) = 0.5e-3*x(t-10)*v(t-10)/(1+0.1e-5*v(t-10))-.3*y(t)-y(t)*z(t);

Eq3 := diff(v(t), t) = 200*y(t-10)-8*v(t);

Eq4 := diff(z(t), t) = 2*y(t)*z(t)-.15*z(t);

ics := x(0) = 1, y(0) = 1, v(0) = 5, z(0) = 1;

Thanks

I am trying to solve the Morrison equation for a normal force acting on a cylinder in a viscous fluid by using the potentional theory. With my limited experience in Maple I do not get why my dubble integral cannot be computed. Any help would be appreciated, tips are also very welkom as I am trying to expand my knowledge of Maple. 

Hi all,

I have lots of contstraint equations group and I want to fund a group of parameters which can fit them. 

For example, these are a simple constraint eqqations group:
eqs:{x1>0, x2>0 x1<1000, x2<1000, x1+x2>300,x1+x2<700}

Through SolveTools library, I can determine whether there is a group of parameters.

with(SolveTools[Inequality]);

LinearMultivariateSystem({x1 > 0, x1+x2 > 300, x2 < 1000, x1+x2 < 700, x2 > 0*x1 and 0*x1 < 1000}, [x1, x2]);

{[{x1 <= 300, 0 < x1}, {x2 < -x1 + 700, 300 - x1 < x2}],[{300 < x1, x1 < 700}, {0 < x2, x2 < -x1 + 700}]}

Then, if I want to find a group of parameter a group of parameters (ex, x1=300, x2=200 in this case), how should I do?

I've got the following four differential equations :

v_x:=diff(x(t),t);
v_y:=diff(y(t),t);
d2v_x:=-((C_d)*rho*Pi*(r^2)*(v_x)*sqrt((v_x)^2 +(v_y)^2))/(2*m);
d2v_y:=-((C_d)*rho*Pi*(r^2)*(v_y)*sqrt((v_x)^2 +(v_y)^2))/(2*m)-g;

and the following initial value conditions:

x(0)=0,y(0)=0,v_x(0)=v0/sqrt(2),v_y(0)=v0/sqrt(2) given v0=65 

I need to solve these using the numeric type and then draw overlaid plots

(i) setting C_d=0

(ii) leaving C_d as a variable

before plotting y(t) vs x(t). The hint for this last part is that the path can be seeing using [x(t),y(t)] instead of [t,y(t)]

I've tried to do it but seemed to have several syntax errors.

I've got the following diff.eq

y'(x)=sin(x*y(x)) given y(0)=1 

and need to solve it numerically which is why I've used:

dy4:=diff(y(x),x);
eqn4:=dy4=sin(x*y(x));
ic1:=y(0)=1;
ans3:=dsolve({eqn4,ic1},y(x),type=numeric);

This code doesn't return a value though and in fact, ans3 is being displayed as a procedure

"ans3:=proc(x_rkf45) ... end proc"

I don't quite understand why and what I need to do to get the required numerical solution

Hello

Could you plese help me to plot my function. i want to plot a function in which variables are have able formatting. I have attache my file.

Thank you.

Download shiboft2.mw

Matlab seems to be pretty strong at doing color plots with separate color bars, e.g.

Is this also possible in Maple and somehow in combination with `plots[surfdata](...,color=zhue,...)`?

In a 3d coordinate system I have a circular spacecurve with z-minimum -4 and z-maximum +4. In the same 3d coordinate system I have a 3d surface plot with z-minimum -0.5 and z-maximum +1.3 . When I choose the color option "Z(Hue)" in order to color-code the z-values on the 3d surface and make the topography more clear, I mostly get a totally green 3d surface. It seems that the color scaling is coupled with the spacecurve with z-values of +-4 . How can I uncouple the color scaling from the spacecurve and couple it with the z-range of the surface, while the color-limits shall be at +-1.3 ?

Hi, I'm a big noob in Maple, so may be the answer is very simple.

Thank you!!!

Download black.mw

Reference: http://www.iflscience.com/physics/beautiful-mathematical-gifs-will-mesmerize-you

I need to find the local maxima and minima of f(x,y)=x(x+y)*e^(y-x). I have tried to look for an appropriate method that I could use to achieve this, but got stuck. I also don't quite understand the math behind tying to obtain the local maxima and  minima for a function of this type.

I'm trying to evaluate the multidimensional limit: 

(1+y)^(x-1)-1/(1-cos((x-1)^2+y^2)^(1/4)) as (x,y)->(1,0) using the limit command :

limit((1+y)^(x-1)/(1-cos((x-1)^2+y^2)^(1/4)),{x=1,y=0});

but don't seem to get any output. Also, I think the limit for this function doesn't exist or is indeterminate on R2. Where am I wrong?

I am considering options to access Maple features from within a Fortran program using the OpenMaple API. I do not find any examples illustrating this (or even precise statements if this is possible in principle). (Quite surprising to me considering the presence of Fortran in scientific computing).

Is the only way to go to write a C wrapper for the API? If yes, is there an example for such a wrapper which performs common conversions between Fortran and C data types.

Thanks!