TY - JOUR

T1 - Closed form solution for the equations of motion for constrained linear mechanical systems and generalizations

T2 - an algebraic approach

AU - Moysis, Lazaros

AU - Pantelous, Athanasios A.

AU - Antoniou, Efstathios

AU - Karampetakis, Nicholas P.

PY - 2017/2/1

Y1 - 2017/2/1

N2 - In this paper, a mathematical methodology is presented for the determination of the solution of motion for linear constrained mechanical systems applicable also to systems with singular coefficients. For mathematical completeness and also to incorporate some other interesting cases, the methodology is formulated for a general class of higher order matrix differential equations. Thus, describing the system in an autoregressive moving average (ARMA) form, the closed form solution is derived in terms of the finite and infinite Jordan pairs of the system׳s polynomial matrix. The notion of inconsistent initial conditions is considered and an explicit formula for the homogeneous system is given. In this respect, the methodology discussed in the present note provides an alternative view to the problem of computation of the response of complex multi-body systems. Two interesting examples are provided and applications of the equation to such systems are illustrated.

AB - In this paper, a mathematical methodology is presented for the determination of the solution of motion for linear constrained mechanical systems applicable also to systems with singular coefficients. For mathematical completeness and also to incorporate some other interesting cases, the methodology is formulated for a general class of higher order matrix differential equations. Thus, describing the system in an autoregressive moving average (ARMA) form, the closed form solution is derived in terms of the finite and infinite Jordan pairs of the system׳s polynomial matrix. The notion of inconsistent initial conditions is considered and an explicit formula for the homogeneous system is given. In this respect, the methodology discussed in the present note provides an alternative view to the problem of computation of the response of complex multi-body systems. Two interesting examples are provided and applications of the equation to such systems are illustrated.

UR - http://www.scopus.com/inward/record.url?scp=85008210338&partnerID=8YFLogxK

U2 - 10.1016/j.jfranklin.2016.11.027

DO - 10.1016/j.jfranklin.2016.11.027

M3 - Article

AN - SCOPUS:85008210338

VL - 354

SP - 1421

EP - 1445

JO - Journal of the Franklin Institute

JF - Journal of the Franklin Institute

SN - 0016-0032

IS - 3

ER -