The construction of optimal modes for exciting oscillation of a two-link physical pendulum
type: Item
instance of: scholarly article
zbMATH Open document ID: 1008.70022
author: Yu. F. Golubev
author: R. Z. Khajrullin
publication date: 2001-12-18T00:00:00Z
Mathematics Subject Classification ID: 70Q05
Mathematics Subject Classification ID: 93C15
zbMATH DE Number: 1683330
zbMATH Keywords: plane two-link pendulum
zbMATH Keywords: optimal oscillation mode
zbMATH Keywords: homogeneous thin rods
zbMATH Keywords: necessary conditions for extremum
zbMATH Keywords: numerical algorithm
zbMATH Keywords: boundary value problem
zbMATH Keywords: Pontryagin maximum principle
MaRDI profile type: Publication
cites work: Q3694127
cites work: Q3029667
cites work: Q3650112
cites work: Q3994636
title: The construction of optimal modes for exciting oscillation of a two-link physical pendulum
published in: Prikladnaya Matematika i Mekhanika
review text: The paper deals with a plane two-link pendulum whose links are homogeneous thin rods. The authors discuss the problem of optimal oscillation mode of the pendulum. The equations of motion are \(\dot K=L(\varphi_1,\varphi_2)\), \(\dot\varphi_1 = K/A(\varphi_2) - C(\varphi_2)u\), \(\dot\varphi_2 = u\), where \(L(\varphi_1,\varphi_2) = k_1\sin\varphi_1 + k_2\sin(\varphi_1 + \varphi_2)\), \(C(\varphi_2) = B(\varphi_2)/A(\varphi_2)\), \(k_1 = -\frac 12 m_1l_1g - m_2l_1g\), \(k_2 = -\frac 12 m_2l_2g\). The initial conditions are \(K(0) = 0\), \(\varphi_1(0)= \varphi_{10}>0\), \(\varphi_2(0)= \varphi_{20}\). The aim is to construct a control \(u(t)\) satisfying the condition \( |u|<c \) and providing at time \(t=T\) the maximal deviation from the vertical line of the first link, i.e. \(F_0 = -\varphi_1(T)\to\max\), while \( F_1 = K(T)=0\). The authors give necessary conditions for extremum, and construct a numerical algorithm to solve the corresponding boundary value problem.
description: scientific article; zbMATH DE number 1683330