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The equations of motion for a rigid body can be obtained from the principles governing the motion of a particle system. Now we will solve with Maple.

(in spanish)


Lenin Araujo Castillo

Corrección ejercico 4


4.- Cada una de las barras mostradas tiene una longitud de 1 m y una masa de 2 kg. Ambas giran en el plano horizontal. La barra AB gira con una velocidad angular constante de 4 rad/s en sentido contrario al de las manecillas del reloj. En el instante mostrado, la barra BC gira a 6 rad/s en sentido contrario al de las manecillas del reloj. ¿Cuál es la aceleración angular de la barra BC?


restart; with(VectorCalculus)



m := 2

L := 1

theta := (1/4)*Pi

a[G] = x*alpha[BC]*r[G/B]-omega[BC]^2*r[G/B]+a[B]NULL


a[B] = x*alpha[AB]*r[B/A]-omega[AB]^2*r[B/A]+a[A]


aA := `<,>`(0, 0, 0)

`&alpha;AB` := `<,>`(0, 0, 0)

rBrA := `<,>`(1, 0, 0)

`&omega;AB` := `<,>`(0, 0, 4)

aB := aA+`&x`(`&alpha;AB`, rBrA)-4^2*rBrA

Vector[column](%id = 4411990810)


`&alpha;BC` := `<,>`(0, 0, `&alpha;bc`)

rGrB := `<,>`(.5*cos((1/4)*Pi), -.5*sin((1/4)*Pi), 0)

aG := evalf(aB+`&x`(`&alpha;BC`, rGrB)-6^2*rGrB, 5)

Vector[column](%id = 4412052178)


usando "(&sum;)M[G]=r[BC] x F[xy]"

rBC := `<,>`(.5*cos((1/4)*Pi), -.5*sin((1/4)*Pi), 0)

Fxy := `<,>`(Fx, -Fy, 0)


`&x`(rBC, Fxy) = (1/12*2)*1^2*`&alpha;bc`

(.2500000000*sqrt(2)*(-.70710*`&alpha;bc`-25.456)+(.2500000000*(57.456-.70710*`&alpha;bc`))*sqrt(2))*e[z] = (1/6)*`&alpha;bc`



"(&sum;)Fx:-Fx=m*ax"           y             "(&sum;)Fy:Fy=m*ay"

ax := -28.728+.35355*`&alpha;bc`



ay := .35355*`&alpha;bc`+12.728



Fx := -2*ax



Fy := 2*ay



`&x`(rBC, Fxy) = (1/12*2)*1^2*`&alpha;bc`

(.2500000000*sqrt(2)*(-.70710*`&alpha;bc`-25.456)+(.2500000000*(57.456-.70710*`&alpha;bc`))*sqrt(2))*e[z] = (1/6)*`&alpha;bc`


.2500000000*sqrt(2)*(-.70710*`&alpha;bc`-25.456)+(.2500000000*(57.456-.70710*`&alpha;bc`))*sqrt(2) = (1/6)*`&alpha;bc`

.2500000000*2^(1/2)*(-.70710*`&alpha;bc`-25.456)+(14.36400000-.1767750000*`&alpha;bc`)*2^(1/2) = (1/6)*`&alpha;bc`



[[`&alpha;bc` = 16.97068481]]





I have been having problems with using the BodePlot function with units:


R1 := 18.2*10^3*Unit('Omega');

R2 := 10^3*Unit('Omega');

C1 := 470*10^(-12)*Unit('F');

C2 := 4.7*10^(-9)*Unit('F');

# wo is in hertz

wo := 1/sqrt(R1*R2*C1*C2);

# Q is unitless

Q := wo*R1*R2*C2/(R1+R2)



sys := TransferFunction(wo^2/(s^2+wo*s/Q+wo^2));


This is the error message I got:

Error, (in Units:-Standard:-+) the units `1` and `Hz` have incompatible dimensions


I think the problem is that the BodePlot function doesn't expect 'wo' to have units.  

So I tried to work around the issue by using the loglogplot but it doesn't seem to like 

complex function even when I used abs to find the magnitude (with or without units).


 Any workaround is appreciated.

Is it possible to solve piecewise differential equations directly instead of separating the pieces and solving them separately.

like for example if i have a two dimensional function f(t,x) whose dynamics is as follows:

dynamics:= piecewise((t,x) in D1, pde1, pde2); where D1 is some region in (t,x)-plane

now is it possible to solve this system with one pde call numerically?

pde(dynamics, boundary conditions, numeric); doesnot work

        i am wording on fluid dynamics, in which i can up a system of nonlinear partial differential equation with i am suppose to solve using implicit keller box method. i need an asistance on how to implement this in maple.

I am trying to solve a set of equations for a Fluid dynamics problem and I cannot get a result...Any ideas why?

rho := 1.184;
nu := 1.562*10^(-5);
ID := .15;
L := 24.5;
Kl := 12.69;
Ho := 50.52;
a := 2.1*10^(-5);
E := 0.1e-2; alpha := 1.05;

sys := {Re = ID*V/nu, hl = (f*L/ID+Kl)*V^2/(2*9.81), Vflow = (1/4)*Pi*ID^2*V, Hrequired = alpha*V^2/(2*9.81)+hl, Hrequired = -a*Vflow^2+Ho, 1/sqrt(f) = -1.8*log[10](6.9/Re+(E/(3.7))^1.11)};

solve(sys*{Re, V, f, hl, Vflow, Hrequired});
Error, (in unknown) invalid input: Utilities:-SetEquations expects its 2nd argument, equations, to be of type set({boolean, algebraic, relation}), but received {{Re = (9603072983/1000000)*V, hl = (5096839959/100000000000)*((1633333333/10000000)*f+1269/100)*V^2, Vflow = (9/1600)*Pi*V, Hrequired = (5351681957/100000000000)*V^2+hl, Hrequired = -(21/1000000)*Vflow^2+1263/25, 1/f^(1/2) = -(9/5)*ln((69/10)/Re+27367561/250000000000)/ln(10)}}




I am trying to solve rigid nody dynamics on Maplesim!! Trying to simulate Gyroscopic Effect.. I want to plot Angular Momentum of that rigid body!!


How do I do this??



Hello all,

I have the state-space form of a dynamics sytem:

X_dot = AX+B.U

Y= C X,

The initial conditions of the outputs (Y0) are also given.

A is 7x7 known matrix,

C is 14x7 known matrix,

B = 0;

The problem is that it's too long to write down every equations (14+7 eqns) and variables in "dsolve" function

Would you please show me the shorter way to solve a very large state-space system?

I really appreciate your help.


so ill preface this by saying my knowledge of DE equations is rusty at best and my knowledge of maple even worse so this may be a stupid question. im trying to model the dynamics of a system and when i solve for the DE equation it's giving me an accleration of zero (plotting a blank graph) when it definitely shouldnt be. ive attached the worksheet.


 Sorry for my english, I'm french! :)

I try to make a modelisation of pedestrian dynamics.



There's someone, (a dot in Maple) at some randomn place in a square.


He want to go to another place.

So, there's 3 dot in Maple:

- S: The start fixed

- X: Mr X who is traveling from S to E

- E: The end fixed

so, without any rule, X is drawing a line from S to E.

I have uploaded to the Maplesoft Application Center a worksheet exploring the orbital dynamics of the recently discovered Kepler 16 system, where a planet orbits a double star. 

Your comments and suggestions will be appreciated.

And so with this provocative title, "pushing dsolve to its limits" I want to share some difficulties I've been having in doing just that. I'm looking at a dynamic system of 3 ODEs. The system has a continuum of stationary points along a line. For each point on the line, there exist a stable (center) manifold, also a line, such that the point may be approached from both directions. However, simulating the converging trajectory has proven difficult.

I have simulated as...


I'm studying many time ago the quantum chemistry of rectivity . so far, I can arrive to news theories from my experince on Maple productcs as they are incorporated in my theoric equations. I have glad  on communicat my previous results on Chemical Reactivity and Uniffied Field. botn of those ara closely related and my purpose is obtain diffusion and comments on these.

- My first paper was on Chemical Reactivity (Kinetics and Dynamics) and...

In this post I will describe a little about the OU course MS325: Computer Algebra, Chaos and Simulations, which I took last year.

MS325 is a level 3 OU applied mathematics course, which means, roughly that it is pitched at the level of a final year mathematics undergraduate. It is split into three components: Computer Algebra, which teaches the use of Maple and Maple programming; Chaos, which teaches dynamical systems, deterministic chaos and fractals, with an emphasis...

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