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Register a new userSills of chaos in the double pendulum's motion
عتبات الفوضى في حركة النواس المضاعف
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درست في هذا البحث حركة النواس المضاعف، حيث كتبت معادلات أولر لاغرانج و معادلات هملتون القانونية. تطرقت أيضا لمحالة الخاصّة التي تكون فيها احدى الزاويتين ثابتة، حيث يسلك النواس المضاعف سلوك نواس بسيط. درست حالة الاهتزازات الصغيرة حيث يتقارب الحلان التحليلي و العددي بشكل كبير جدا، و ذلك من أجل كتل و أطوال غير متساوية بالضرورة.
In this paper, I study the motion of the double pendulum . I write the Euler -Lagrange equations and canonical Hamilton's equations. I study the special case in which one angle is constant, where the double pendulum behaves as a simple pendulum. I also mention small oscillator's case, where the numerical solution converges to the analytical solution, for unequal lengths and masses.
References used
ALI, M . SAHAL, M, Local Lyapunov Exponents and Characteristics of Fixed /Periodic Points Embedded within a Chaotic Attractor, Journal of Zhejiang university science, India, 2005
AWAIS, M. The Double Pendulum Numerical Analysis of Chaos, Journal of Zhejiang university science, India, 2011
CARL, W.A. The Chaotic Motion of the Double Pendulum, 2012
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