Boundary control in critical time by elastic forces applied at two ends of an inhomogeneous rod for the case in which the wave propagation time over each of the inhomogeneity parts is the same

被引：0

作者：

Belikov, A. V. ^{[1
]}

机构：

[1] Moscow MV Lomonosov State Univ, Moscow, Russia

来源：

DIFFERENTIAL EQUATIONS | 2013年 / 49卷 / 06期

关键词：

Critical Time; Matching Condition; Boundary Control; Elastic Force; Terminal Velocity;

D O I：

10.1134/S0012266113060086

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study boundary control in critical time by elastic forces at two ends of an inhomogeneous rod consisting of two parts of distinct densities and elasticities for the case in which the wave propagation time over each of these parts is the same. We present a closed-form expression for the boundary control by elastic forces bringing the originally quiescent stick into a given terminal state specified by a given terminal displacement and a given terminal velocity in a given critical time.

引用

页码：744 / 749

页数：6

共 9 条

[1] Boundary control in critical time by elastic forces applied at two ends of an inhomogeneous rod for the case in which the wave propagation time over each of the inhomogeneity parts is the same
A. V. Belikov
Differential Equations, 2013, 49 : 744 - 749
[2] Critical-Time Boundary Displacement Control at Two Ends of an Inhomogeneous Rod in the Case of Coincidence of the Wave Propagation Times through Each of Two Homogeneous Parts
Belikov, A. V.
DIFFERENTIAL EQUATIONS, 2013, 49 (11) : 1336 - 1346
[3] Critical-time boundary displacement control at two ends of an inhomogeneous rod in the case of coincidence of the wave propagation times through each of two homogeneous parts
A. V. Belikov
Differential Equations, 2013, 49 : 1336 - 1346
[4] Boundary control by an elastic force at one end of an inhomogeneous rod with the other end free for the case in which the wave travels either of the homogeneous parts in the same time
A. V. Belikov
Differential Equations, 2011, 47 : 402 - 411
[5] Boundary Control by an Elastic Force at One End of an Inhomogeneous Rod with the Other End Free for the Case in Which the Wave Travels Either of the Homogeneous Parts in the Same Time
Belikov, A. V.
DIFFERENTIAL EQUATIONS, 2011, 47 (03) : 402 - 411
[6] Optimization of the control by elastic boundary forces at two ends of a string in an arbitrarily large time interval
Il'in, V. A.
Moiseev, E. I.
DIFFERENTIAL EQUATIONS, 2008, 44 (01) : 92 - 114
[7] Optimization of the control by elastic boundary forces at two ends of a string in an arbitrarily large time interval
V. A. Il’in
E. I. Moiseev
Differential Equations, 2008, 44 : 92 - 114
[8] Boundary control by displacements at one endpoint of an inhomogeneous rod for fixed other endpoint in the case of coinciding times of passage of the wave through either of the inhomogeneity parts
Belikov, A. V.
DIFFERENTIAL EQUATIONS, 2010, 46 (08) : 1178 - 1187
[9] Boundary control by displacements at one endpoint of an inhomogeneous rod for fixed other endpoint in the case of coinciding times of passage of the wave through either of the inhomogeneity parts
A. V. Belikov
Differential Equations, 2010, 46 : 1178 - 1187

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