Hi,
Thanks for your reply.
The Hamitonian H which I am writing is the restatement of the energybalance of the system. Since there is no damping, the inputted energy should be equal to the sum of the potential energy and the kinetic energy at any state of oscillation of the system...
Hi Thanks Dalespam,
Actually, I am facing trouble in solving certain dynamical system. You can refer to my new thread titled "Discrepancy in the solution of a nonlinear dynamical system".
Hi,
I am solving the following nonlinear dynamical system using Energy Balance Method (EBM*). My intention is to arrive at an approximate analytical expression for the frequency of oscillation and the excitation force.
u''+u=A(1+2*u) with u(0)=u'(0)=0, where A is a constant (Physically it...
Hi,
I need some help in writing the Hamiltonian function for the following dynamical systems.
1) u''+u=A (1+2*u+3*u^2)
2) u''+u=A/((1-u)^2);
In both cases A is a constant and u is a function of t.
Any help would be greatly appreciated.
Thank you.
Manish
Hi,
A is a constant.
I will also comment on the qualitative behavior of the system.
for extremely small values of A, the system has oscillation frequency equal to 1, which is evident from the Differential Equation.
As the value of A is increased oscillation frequency decreases
At...
Hi,
Thanks for the reply.
The term omega, although not explicitly found in the differential equation. represents the frequency of oscillation.
When A is zero, the RHS of the equation is zero and the frequency of oscillation is equal to 1, which indicates that the period is equal to 2*pi...
Hi,
I am trying to solve the following differential equation using the variational iteration method:
u''+u=A/((1-u)^2) with initial conditions, u(0)=u'(0)=0.
My ultimate aim is to obtain the relation between A and w (i.e. omega).
A is a Heaviside step function i.e. A(t)=A*H(t)...