Advanced Search

Hamza Rafiq

30 Reputation

3 Badges

0 years, 190 days
Contact Hamza Rafiq

MaplePrimes Activity


These are questions asked by Hamza Rafiq

Poincare Section diagram for pendulum ...

Hamza Rafiq 30 Maple 18
differential-equations pendulum dynamical-systems
March 11 2025
2 0

I am trying to draw the Poincare section diagram related pendulum problem, article is shared below. I can not understand and code gives error, can you help me to draw Poincare section Fig. 4 of attached article?7._Energy_distribution_in_intrinsically_coupled_system [moderator: URL changed to respect IP, as per Mapleprimes Terms of Use]

pendulum.mw

How can we collect coefficients of diffe...

Hamza Rafiq 30 Maple 18
homework collect differential-equations
February 14 2025
1 1

How can we collect coefficients of different powers of involved variables form Eq, to get system of algebraic equations, like x,y,z,t but these are also appear in JacobiCN function? Maple file link is attached below, please help me to solve this issue. 

collection_of_coefficients.mw

How to remove quadratic singularity in d...

Hamza Rafiq 30 Maple 18
ode differential-equations singularity
January 20 2025
1 2

I am trying to find the phase portraits of a dynamical system; couples ODE system but it appears in singular form. How can we remove the singularity of coupled ODE system in P and W depending on \xi, where \alpha is scalar and v is velocity.

How remove quadratic singularity to make this system Hamiltonian in below coupled ODE system in P & W.

 singular_system.mw

> 

restart
> 

with(PDEtools):
> 

alias(P = P(xi), W = W(xi))

P, W

 (1)
> 

rf1 := diff(P, xi) = W

diff(P, xi) = W

 (2)
> 

rf2 := diff(W, xi) = (P-(alpha^2+1)*P*W^2)/(v+(1/2*(alpha^2+1))*P^2)

diff(W, xi) = (P-(alpha^2+1)*P*W^2)/(v+(1/2)*(alpha^2+1)*P^2)

 (3)
 

 

Download singular_system.mw

Real and Imaginary components of complex...

Hamza Rafiq 30 Maple 18
complex homework pde
January 16 2025
1 2

Hello, I need help to find the real and Imaginary components of following complex model using maple, here q=u+iv,

How to solve a system of equations invol...

Hamza Rafiq 30 Maple 18
homework pde pdsolve
January 13 2025
1 6

Hello everyone, I am facing problem to solve a system of partial differential equations of f, g & q in three variables x,y,t. I have attached the maple file and also a page that i am exploring, in attcahed page I need to find results given in (7) and (8). Maple file is also attached below, please help me to solve this system of PDEs for required results given in (7) and (8). Thanks
 


 

Download PDEs_system_solution.mw

> 

restart
> 

with(PDEtools):
> 

alias(u = u(x, y, t), f = f(x, y, t), g = g(x, y, t), q = q(x, y, t))

u, f, g, q

 (1)

eq1 := 24*g*(diff(q, y))*(diff(q, x))^3-12*(diff(q, y))*(diff(q, x))^2*g^2 = 0

24*g*(diff(q, y))*(diff(q, x))^3-12*(diff(q, y))*(diff(q, x))^2*g^2 = 0

 (2)

eq2 := 60*g*sigma*(diff(q, y))*(diff(q, x))^3-30*sigma*(diff(q, y))*(diff(q, x))^2*g^2+18*(diff(g, x))*(diff(q, y))*(diff(q, x))^2-15*(diff(q, y))*(diff(q, x))*(diff(g, x))*g+18*g*(diff(q, y))*(diff(q, x))*(diff(q, x, x))-3*(diff(q, y))*g^2*(diff(q, x, x))+6*(diff(g, y))*(diff(q, x))^3+18*g*(diff(q, x))^2*(diff(q, y, x))-9*(diff(g, y))*g*(diff(q, x))^2-3*g^2*(diff(q, x))*(diff(q, y, x)) = 0

60*g*sigma*(diff(q, y))*(diff(q, x))^3-30*sigma*(diff(q, y))*(diff(q, x))^2*g^2+18*(diff(g, x))*(diff(q, y))*(diff(q, x))^2-15*(diff(q, y))*(diff(q, x))*(diff(g, x))*g+18*g*(diff(q, y))*(diff(q, x))*(diff(diff(q, x), x))-3*(diff(q, y))*g^2*(diff(diff(q, x), x))+6*(diff(g, y))*(diff(q, x))^3+18*g*(diff(q, x))^2*(diff(diff(q, x), y))-9*(diff(g, y))*g*(diff(q, x))^2-3*g^2*(diff(q, x))*(diff(diff(q, x), y)) = 0

 (3)

eq3 := 36*g*sigma*(diff(q, y))*(diff(q, x))*(diff(q, x, x))-27*sigma*(diff(q, y))*(diff(q, x))*(diff(g, x))*g-3*(diff(q, y))*(diff(g, x))^2+6*(diff(g, y, x))*(diff(q, x))^2-9*(diff(g, y))*(diff(g, x))*(diff(q, x))+2*g*(diff(q, y))*(diff(q, t))+2*g*(diff(q, y))*(diff(q, x, x, x))-6*(diff(f, y))*(diff(q, x))^2*g+12*(diff(g, y))*sigma*(diff(q, x))^3+6*(diff(g, x))*(diff(q, y))*(diff(q, x, x))-3*(diff(q, y, x))*(diff(g, x))*g-3*(diff(q, y))*(diff(g, x, x))*g+6*(diff(q, y))*(diff(g, x, x))*(diff(q, x))-3*(diff(q, x, x))*(diff(g, y))*g-3*g*(diff(q, x))*(diff(g, y, x))+12*(diff(q, x))*(diff(g, x))*(diff(q, y, x))+6*g*(diff(q, y, x))*(diff(q, x, x))+6*(diff(q, x))*g*(diff(q, y, x, x))+6*(diff(g, y))*(diff(q, x))*(diff(q, x, x))-6*sigma*(diff(q, x))*(diff(q, y, x))*g^2+50*g*sigma^2*(diff(q, y))*(diff(q, x))^3-24*sigma^2*(diff(q, y))*(diff(q, x))^2*g^2+36*(diff(g, x))*sigma*(diff(q, y))*(diff(q, x))^2-15*(diff(q, x))^2*sigma*(diff(g, y))*g-6*(diff(f, x))*(diff(q, y))*(diff(q, x))*g-6*sigma*(diff(q, y))*(diff(q, x, x))*g^2+36*g*sigma*(diff(q, x))^2*(diff(q, y, x)) = 0

50*g*sigma^2*(diff(q, y))*(diff(q, x))^3-24*sigma^2*(diff(q, y))*(diff(q, x))^2*g^2+36*(diff(g, x))*sigma*(diff(q, y))*(diff(q, x))^2-15*(diff(q, x))^2*sigma*(diff(g, y))*g-6*(diff(f, x))*(diff(q, y))*(diff(q, x))*g-6*sigma*(diff(q, x))*(diff(diff(q, x), y))*g^2-6*sigma*(diff(q, y))*(diff(diff(q, x), x))*g^2+36*g*sigma*(diff(q, x))^2*(diff(diff(q, x), y))-3*(diff(q, y))*(diff(g, x))^2+6*(diff(diff(g, x), y))*(diff(q, x))^2+6*(diff(g, y))*(diff(q, x))*(diff(diff(q, x), x))+6*(diff(g, x))*(diff(q, y))*(diff(diff(q, x), x))-3*(diff(diff(q, x), y))*(diff(g, x))*g-3*(diff(q, y))*(diff(diff(g, x), x))*g+6*(diff(q, y))*(diff(diff(g, x), x))*(diff(q, x))-3*(diff(diff(q, x), x))*(diff(g, y))*g-3*g*(diff(q, x))*(diff(diff(g, x), y))+12*(diff(q, x))*(diff(g, x))*(diff(diff(q, x), y))+6*g*(diff(diff(q, x), y))*(diff(diff(q, x), x))+6*(diff(q, x))*g*(diff(diff(diff(q, x), x), y))+2*g*(diff(q, y))*(diff(diff(diff(q, x), x), x))+2*g*(diff(q, y))*(diff(q, t))+12*(diff(g, y))*sigma*(diff(q, x))^3-9*(diff(g, y))*(diff(g, x))*(diff(q, x))-6*(diff(f, y))*(diff(q, x))^2*g-27*sigma*(diff(q, y))*(diff(q, x))*(diff(g, x))*g+36*g*sigma*(diff(q, y))*(diff(q, x))*(diff(diff(q, x), x)) = 0

 (4)

eq4 := -3*g*(diff(f, y))*(diff(q, x, x))-3*(diff(q, y))*g*(diff(f, x, x))-3*g*(diff(q, x))*(diff(f, y, x))-3*g*(diff(q, y, x))*(diff(f, x))+15*g*sigma^3*(diff(q, y))*(diff(q, x))^3-6*sigma^3*(diff(q, y))*(diff(q, x))^2*g^2+21*(diff(g, x))*sigma^2*(diff(q, y))*(diff(q, x))^2-6*(diff(q, x))^2*sigma^2*(diff(g, y))*g-9*(diff(f, y))*(diff(q, x))^2*sigma*g+3*g*sigma*(diff(q, y))*(diff(q, t))-9*sigma*(diff(q, x))*(diff(g, x))*(diff(g, y))+9*(diff(g, y, x))*sigma*(diff(q, x))^2+7*(diff(g, y))*sigma^2*(diff(q, x))^3-3*sigma*(diff(q, y))*(diff(g, x))^2-6*(diff(g, x))*(diff(q, x))*(diff(f, y))-3*(diff(q, y))*(diff(g, x))*(diff(f, x))-3*(diff(g, y))*(diff(q, x))*(diff(f, x))-3*(diff(g, y, x))*(diff(g, x))-3*(diff(g, x, x))*(diff(g, y))+g*(diff(q, y, t))+9*g*sigma*(diff(q, y, x))*(diff(q, x, x))-3*sigma*(diff(q, x, x))*(diff(g, y))*g+9*sigma*(diff(q, x))*g*(diff(q, y, x, x))-3*sigma*(diff(q, y, x))*(diff(g, x))*g-3*sigma*(diff(q, x))*(diff(g, y, x))*g+9*(diff(g, y))*sigma*(diff(q, x))*(diff(q, x, x))+9*(diff(g, x))*sigma*(diff(q, y))*(diff(q, x, x))+3*g*sigma*(diff(q, y))*(diff(q, x, x, x))+18*sigma*(diff(q, x))*(diff(g, x))*(diff(q, y, x))+21*g*sigma^2*(diff(q, x))^2*(diff(q, y, x))-3*sigma^2*(diff(q, x))*(diff(q, y, x))*g^2+9*sigma*(diff(q, y))*(diff(g, x, x))*(diff(q, x))-3*sigma*(diff(q, y))*(diff(g, x, x))*g-3*sigma^2*(diff(q, y))*(diff(q, x, x))*g^2+21*g*sigma^2*(diff(q, y))*(diff(q, x))*(diff(q, x, x))-9*(diff(f, x))*(diff(q, y))*(diff(q, x))*sigma*g-12*sigma^2*(diff(q, y))*(diff(q, x))*(diff(g, x))*g+(diff(q, y))*(diff(g, t))+(diff(g, y))*(diff(q, t))+3*(diff(g, x, x))*(diff(q, y, x))+(diff(q, y))*(diff(g, x, x, x))+3*(diff(q, x))*(diff(g, y, x, x))+(diff(q, y, x, x, x))*g+3*(diff(g, x))*(diff(q, y, x, x))+(diff(g, y))*(diff(q, x, x, x))+3*(diff(g, y, x))*(diff(q, x, x)) = 0

7*(diff(g, y))*sigma^2*(diff(q, x))^3-3*sigma*(diff(q, y))*(diff(g, x))^2-6*(diff(g, x))*(diff(q, x))*(diff(f, y))-3*(diff(q, y))*(diff(g, x))*(diff(f, x))-3*(diff(g, y))*(diff(q, x))*(diff(f, x))-3*(diff(q, y))*g*(diff(diff(f, x), x))-3*g*(diff(q, x))*(diff(diff(f, x), y))-3*g*(diff(f, y))*(diff(diff(q, x), x))-3*g*(diff(diff(q, x), y))*(diff(f, x))+9*(diff(diff(g, x), y))*sigma*(diff(q, x))^2+15*g*sigma^3*(diff(q, y))*(diff(q, x))^3-6*sigma^3*(diff(q, y))*(diff(q, x))^2*g^2+21*(diff(g, x))*sigma^2*(diff(q, y))*(diff(q, x))^2-6*(diff(q, x))^2*sigma^2*(diff(g, y))*g-9*(diff(f, y))*(diff(q, x))^2*sigma*g+3*g*sigma*(diff(q, y))*(diff(q, t))-9*sigma*(diff(q, x))*(diff(g, x))*(diff(g, y))+9*g*sigma*(diff(diff(q, x), y))*(diff(diff(q, x), x))-3*sigma*(diff(diff(q, x), x))*(diff(g, y))*g+9*sigma*(diff(q, x))*g*(diff(diff(diff(q, x), x), y))-3*sigma*(diff(diff(q, x), y))*(diff(g, x))*g-3*sigma*(diff(q, x))*(diff(diff(g, x), y))*g+9*(diff(g, y))*sigma*(diff(q, x))*(diff(diff(q, x), x))+9*(diff(g, x))*sigma*(diff(q, y))*(diff(diff(q, x), x))+3*g*sigma*(diff(q, y))*(diff(diff(diff(q, x), x), x))+18*sigma*(diff(q, x))*(diff(g, x))*(diff(diff(q, x), y))+21*g*sigma^2*(diff(q, x))^2*(diff(diff(q, x), y))-3*sigma^2*(diff(q, x))*(diff(diff(q, x), y))*g^2+9*sigma*(diff(q, y))*(diff(diff(g, x), x))*(diff(q, x))-3*sigma*(diff(q, y))*(diff(diff(g, x), x))*g-3*sigma^2*(diff(q, y))*(diff(diff(q, x), x))*g^2-9*(diff(f, x))*(diff(q, y))*(diff(q, x))*sigma*g-12*sigma^2*(diff(q, y))*(diff(q, x))*(diff(g, x))*g+21*g*sigma^2*(diff(q, y))*(diff(q, x))*(diff(diff(q, x), x))+(diff(q, y))*(diff(g, t))+(diff(g, y))*(diff(q, t))-3*(diff(diff(g, x), y))*(diff(g, x))-3*(diff(diff(g, x), x))*(diff(g, y))+g*(diff(diff(q, t), y))+3*(diff(diff(g, x), x))*(diff(diff(q, x), y))+(diff(q, y))*(diff(diff(diff(g, x), x), x))+3*(diff(q, x))*(diff(diff(diff(g, x), x), y))+(diff(diff(diff(diff(q, x), x), x), y))*g+3*(diff(g, x))*(diff(diff(diff(q, x), x), y))+(diff(g, y))*(diff(diff(diff(q, x), x), x))+3*(diff(diff(g, x), y))*(diff(diff(q, x), x)) = 0

 (5)

eq5 := (diff(g, y))*sigma*(diff(q, t))+(diff(g, t))*sigma*(diff(q, y))+(diff(g, y))*sigma^3*(diff(q, x))^3+3*(diff(g, x))*sigma^3*(diff(q, y))*(diff(q, x))^2+g*sigma^2*(diff(q, y))*(diff(q, t))+g*sigma^4*(diff(q, y))*(diff(q, x))^3-3*(diff(f, x))*sigma*(diff(q, y))*(diff(g, x))-3*(diff(f, x))*sigma*(diff(q, x))*(diff(g, y))-6*(diff(f, y))*sigma*(diff(q, x))*(diff(g, x))+3*g*sigma^3*(diff(q, x))^2*(diff(q, y, x))+g*sigma^2*(diff(q, y))*(diff(q, x, x, x))-3*(diff(f, x))*sigma*(diff(q, y, x))*g-3*(diff(f, y))*sigma*(diff(q, x, x))*g-3*g*sigma*(diff(q, y))*(diff(f, x, x))-3*sigma*(diff(q, x))*g*(diff(f, y, x))+3*(diff(g, x, x))*sigma^2*(diff(q, y))*(diff(q, x))+6*(diff(g, x))*sigma^2*(diff(q, x))*(diff(q, y, x))+diff(g, y, t)-3*(diff(f, x))*(diff(q, y))*(diff(q, x))*sigma^2*g+3*g*sigma^3*(diff(q, y))*(diff(q, x))*(diff(q, x, x))+3*g*sigma^2*(diff(q, x))*(diff(q, y, x, x))-3*(diff(f, y))*(diff(q, x))^2*sigma^2*g+3*(diff(g, y))*sigma^2*(diff(q, x))*(diff(q, x, x))+3*g*sigma^2*(diff(q, y, x))*(diff(q, x, x))+3*(diff(g, x))*sigma^2*(diff(q, y))*(diff(q, x, x))-3*(diff(g, y))*(diff(f, x, x))-3*(diff(f, y))*(diff(g, x, x))-3*(diff(g, x))*(diff(f, y, x))-3*(diff(f, x))*(diff(g, y, x))+diff(g, y, x, x, x)+3*(diff(g, y, x))*sigma^2*(diff(q, x))^2+3*(diff(g, x, x))*sigma*(diff(q, y, x))+3*(diff(g, y, x, x))*sigma*(diff(q, x))+(diff(g, x, x, x))*sigma*(diff(q, y))+g*sigma*(diff(q, y, t))+3*(diff(g, x))*sigma*(diff(q, y, x, x))+3*(diff(g, y, x))*sigma*(diff(q, x, x))+g*sigma*(diff(q, y, x, x, x))+(diff(g, y))*sigma*(diff(q, x, x, x)) = 0

(diff(g, t))*sigma*(diff(q, y))+(diff(g, y))*sigma^3*(diff(q, x))^3+(diff(g, y))*sigma*(diff(q, t))+3*(diff(diff(g, x), y))*sigma^2*(diff(q, x))^2+3*(diff(diff(g, x), x))*sigma*(diff(diff(q, x), y))+3*(diff(diff(diff(g, x), x), y))*sigma*(diff(q, x))+(diff(diff(diff(g, x), x), x))*sigma*(diff(q, y))+g*sigma*(diff(diff(q, t), y))+3*(diff(g, x))*sigma*(diff(diff(diff(q, x), x), y))+3*(diff(diff(g, x), y))*sigma*(diff(diff(q, x), x))+g*sigma*(diff(diff(diff(diff(q, x), x), x), y))+(diff(g, y))*sigma*(diff(diff(diff(q, x), x), x))-3*(diff(f, x))*(diff(q, y))*(diff(q, x))*sigma^2*g+3*g*sigma^3*(diff(q, y))*(diff(q, x))*(diff(diff(q, x), x))-3*(diff(f, y))*(diff(q, x))^2*sigma^2*g+6*(diff(g, x))*sigma^2*(diff(q, x))*(diff(diff(q, x), y))+3*g*sigma^2*(diff(q, x))*(diff(diff(diff(q, x), x), y))+3*(diff(g, y))*sigma^2*(diff(q, x))*(diff(diff(q, x), x))+3*g*sigma^2*(diff(diff(q, x), y))*(diff(diff(q, x), x))+3*(diff(g, x))*sigma^2*(diff(q, y))*(diff(diff(q, x), x))+3*g*sigma^3*(diff(q, x))^2*(diff(diff(q, x), y))+g*sigma^2*(diff(q, y))*(diff(diff(diff(q, x), x), x))-3*(diff(f, x))*sigma*(diff(diff(q, x), y))*g-3*(diff(f, y))*sigma*(diff(diff(q, x), x))*g-3*g*sigma*(diff(q, y))*(diff(diff(f, x), x))-3*sigma*(diff(q, x))*g*(diff(diff(f, x), y))+3*(diff(diff(g, x), x))*sigma^2*(diff(q, y))*(diff(q, x))+3*(diff(g, x))*sigma^3*(diff(q, y))*(diff(q, x))^2+g*sigma^2*(diff(q, y))*(diff(q, t))+g*sigma^4*(diff(q, y))*(diff(q, x))^3-3*(diff(f, x))*sigma*(diff(q, y))*(diff(g, x))-3*(diff(f, x))*sigma*(diff(q, x))*(diff(g, y))-6*(diff(f, y))*sigma*(diff(q, x))*(diff(g, x))+diff(diff(g, t), y)+diff(diff(diff(diff(g, x), x), x), y)-3*(diff(g, y))*(diff(diff(f, x), x))-3*(diff(f, y))*(diff(diff(g, x), x))-3*(diff(g, x))*(diff(diff(f, x), y))-3*(diff(f, x))*(diff(diff(g, x), y)) = 0

 (6)

eq6 := -3*(diff(f, x))*(diff(f, y, x))-3*(diff(f, y))*(diff(f, x, x))+diff(f, y, x, x, x)+diff(f, y, t) = 0

-3*(diff(f, x))*(diff(diff(f, x), y))-3*(diff(f, y))*(diff(diff(f, x), x))+diff(diff(diff(diff(f, x), x), x), y)+diff(diff(f, t), y) = 0

 (7)
> 

pdsolve({eq1, eq2, eq3, eq4, eq5, eq6}, {f, g, q})

``

Download PDEs_system_solution.mw

Page 1 of 1