Exact solution of Euler's equations in the case of non-zero applied torques (rigid body dynamics): reduction to Abel ordinary differential equation

Details Exact solution of Euler's equations in the case of non-zero applied torques (rigid body dynamics): reduction to Abel ordinary differential equation Exact solution of Euler's equations in the case of non-zero applied torques (rigid body dynamics): reduction to Abel ordinary differential equation

2011-01-09

arxiv.org/abs/1101.1670v1

Physics

General Physics

5 pages

Scientific paper

Here is presented a new exact solution of Euler's equations (rigid body dynamics, non-zero applied torques) in the case of reduction one of Euler's equations to a proper Abel ordinary differential equation. One component of angular velocity of rigid body for such a solution - is a proper classical solution for the case of symmetric rigid rotor (which has two equal moments of inertia), but applied torques is not zero. The 2-nd component is proved to be appropriate solution of Abel ordinary differential equation. Due to a very special character of Riccati's type equation (such as Abel ODE), its general solution is known to have a proper gap of above component of angular velocity of rigid body. It means a possibility of sudden acceleration of rigid body rotation around appropriate principal axe at definite moment of parametrical time. The 3-d could be obtained from a simple algebraic equality. It is a multiplying all the components of angular velocity of rigid body (which is to be a constant for such a solution).

Affiliated with

Also associated with

No associations

Rating

Exact solution of Euler's equations in the case of non-zero applied torques (rigid body dynamics): reduction to Abel ordinary differential equation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Exact solution of Euler's equations in the case of non-zero applied torques (rigid body dynamics): reduction to Abel ordinary differential equation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Exact solution of Euler's equations in the case of non-zero applied torques (rigid body dynamics): reduction to Abel ordinary differential equation will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-455068