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0101/201/20000001/301/30eud ey01/501/5e”22c￡hkhhehk3△guhk3∑g1hk3hk5∑mh5∑g21h5∑k2hk5∑g2hkk=07∑8hk心∑g1hk∑g2hk7∑g3hkaei≥i回p-p i-c2i 2=i-j 2p￡1p=0t2t-2k≠i-j 2p￡-p=02t-ea2=5/2ee”23￡e中国煤化工￡wn￡y=￡u11cnmhgm2eo0elone1 ueeez26e8%4 ha7aa"￡dtec se te@ 1 s1 iaah nsns士2000ae叫21%x"te0=t2/2 1120010,1四an016μae土 rains>u.0uans0e2,土10ns36°aece 972 majid k i. forces and deflexions in changing structures. the structural engineerft97225c3203 arutyunyan n khf-naumoy v e. the boundary value problem of the theory of viscoelastic-plasticity of a growingbody subject to aging. j appl math mechf-1984e48ifef4 abramowitz me -stegun i a, handbook of mathematical functionse-washington dce national bureau of standards5 gradshetyn i se-ryzhik i m. tables of integralsf-teries and products. new yorkfacademic pressf-1979solution of time- variation dynamic problemby legendre polynomialscao zhiyuanang shougaoe"department of engineering mechanics f-tongji universityf-shanghaif-20009220abstract the problem of time-variation dynamic systems may be induced to solve a group of differential equations with time-variation coefficients. the state space approach combined with the legendre polynomials and its operational integration matrix is employed for the analysis of time-variation dynamic systems in this paperf and the generalized formulation of the solution is also given. so the basisof efficient method to solve the time-variation mechanical problems is establishede and is beneficial tofurther research of time-variation sciencekey words time-variation dynamicsf-legendre polynomials state space equatione - operationalntegration matrix12av4 asee"e0=∑-pi-tp2i-2j 4p 12i 2 1)s-,“i≥je"a1e0中国煤化工￡¨a2e0cnmhge¨a1eee001e8ce00a7y0eag±e"i≥0片方数围2 27 1k=(2-1 2121p=0e13分eak≠i-j 2p2p=0e2e-2