Here we present the derivation of the new set of equations termed， Lorentz transformations， and all the subsequent LORENTZ TRANSFORMATIONSWe consider two coordinate systems (frames of reference) one stationary S and one moving at some velocity v relative to S， then according to the two postulates of Relativity， stated in the main text， the displacement in both frames is of the same Therefore， we have (A-1) (A-2)We should note here that in the old Galilean transformations these equations would be (A-3)which is in direct contradiction to Postulate 2， a firm experimental Equations (A-1) and (A-2) can be written as(A-4) (A-5)That is， (A-6)We are interested in finding and in terms of x and That is， = (x， t) (A-7) = (x， t) (A-8)This is accomplished via the formation of two linear simultaneous equations as follows:(A-9) (A-10)where a11， a12， a21， and a22 are constants to be It is required that the transformations are linear in order for one event in one system to be interpreted as one event in the other system; quadratic transformations imply more than one event in the other Solution of problems involving motion begins with an assumption of their initial conditions; ， where does the problem begin?The classical assumption is to set = 0 at = Therefore， according to S， the system appears to be moving with a velocity v， so that x = We can obtain this from E (A-9) by writing it in the form = a11(x - vt) so that， when = 0， x = Therefore， we conclude that a12 = - We can write Equations (A-9) and (A-10) as (A-11) (A-12)Substituting and into Equation (A-6) and rearranging， we get (A-13)Since this equation is equal to zero， all the coefficients must That is，(A-14) (A-15) (A-16)Solving these equations we obtain(A-17) (A-18)where β = v/c and Thus， substituting these values in E (A-11) and (A-12) we obtain the famous Lorentz coordinate transformation equations connecting the fixed coordinate system S to the moving coordinate system :(A-19) (A-20)We may also obtain the inverse transformations (from system to S) by replacing v by –v and simply interchanging primed and unprimed This gives，(A-21) (A-22)VELOCITY TRANSFORMATIONSAs a direct consequence to these new transformations， all the other mathematical operations and physical variables follow For example， the velocity equations (though still the derivatives of the displacement) assume a new form， so the Lorentz form of the velocities is:From E (A-19) and (A-20) we have: (A-23) (A-24)Therefore:(A-25)ENERGY CONSIDERATIONSConsider a particle of rest mass m0 being acted by a force F through a distance x in time t and that it attains a final velocity The kinetic energy attained by the particle is defined as the work done by the force F The applicable equations are，(A-26)We note thatand thatSubstituting d(γv) in E (45) and integrating， we obtain (A-27)That is， (A-28)This says that K = (m – m0)c2 and finally one sees that the total energy is equal to the sum of the kinetic energy K and the rest energy E0 = ， E = K + Eo = γm0c2 = γE0， (A-29) where E0 = m0c2 and E = 给分吧
液晶材料的分类、应用及其发展状况摘要介绍了液晶材料的种类及其分类性能，论述了液晶材料的应用和发展情况。关键词液晶材料;介晶相;应用液晶的简介和分类液晶是一些化合物所具有的介于固态晶体的三维有序和无规液态之间的一种中间相态，又称作介晶相，是一种取向有序流体，既具有液体的易流动性，又有晶体的双折射等各向异性的特征。1888年奥地利植物学家Reinitzer首次发现液晶，但直到1941年Kargin提出液晶态是聚合物体系的一种普遍存在状态，人们才开始了对高分子液晶的研究。近二十多年来液晶材料获得迅速的发展，这是因为液晶材料的光电效应被发现，因此被广泛地应用在需低电压和轻薄短小的显示组件上，因此它一跃成为一热门的科学研究及应用的主题，目前已被广泛使用于电子表、电子计算器和计算机显示屏幕上，液晶逐渐成为显示工业上不可或缺的重要材料，液晶高分子的大规模研究工作起步更晚，但目前已发展为液晶领域中举足轻重的部分。如果说小分子液晶是有机化学和电子学之间的边缘科学，那么液晶高分子则牵涉到高分子科学、材料科学、生物工程等多门科学，而且在高分子材料、生命科学等方面都得到了大量应用。1溶致型液晶有些材料在溶剂中，处于一定的浓度区间内会产生液晶，这类液晶我们叫它溶致液晶。如可以利用溶致型液晶聚合物的液晶相的高浓度低黏度特性进行液晶纺丝制备强度高模量的纤维。溶致型液晶材料广泛存在于自然界、生物体中，与生命息息相关，但在显示中尚无应用。2热致型液晶热致型液晶分子会随温度上升而伴随一连串相转移，即由固体变成液晶状态，最后变成等向性液体，在这些相变化的过程中液晶分子的物理性质都会随之变化，如折射率、介电异向性、弹性系数和粘度等。在热致型液晶中，又根据液晶分子排列结构分为三大类：近晶相、向列相和胆甾相。1近晶型液晶近晶相除有沿分子长轴的取向有序外，有一个沿某一方向的平移有序，近晶型液晶在所有液晶聚合态结构中最接近固体晶体，通常含有C=N或者N=N键及苯环结构，分子是厂棒状。目前各近晶相中的手性近晶C相，即铁电相引起人们广泛兴趣。铁电液晶具备向列相液晶所不具备的高速度（微秒级）和记忆性的优异特征，它们在最近几年得到大量研究。2向列型液晶向列相仅有沿分子长轴的取向有序，液晶分子呈棒状形刚性部分平行排列，该种液晶分子运动自由度大，是流动性最好的液晶，此类型液晶的粘度小，应答速度快，是最早被应用的液晶，普遍地使用于液晶电视、笔记本电脑以及各类型显示元件上。3胆甾型液晶这类液晶大都是胆甾醇的衍生物，胆甾醇本身无液晶性质，而它的衍生物均具有液晶特性，次类型液晶是由多层相列型液晶堆积所形成，为向列相液晶的一种，也可以称为旋光性的向列相液晶，因分子具有非对称碳中心，所以分子的排列呈螺旋平面状的排列，面和面之间为相互平行，而分子在各平面上为向列相。液晶的应用及发展状况1液晶材料在显示器的应用回顾液晶的发展史可以发现，尽管液晶早在19世纪60年代已经被发现，然而在相当长一段时间里，虽然液晶的许多有价值的现象早被揭露，但液晶始终只是实验室中的珍品而已。只有当液晶被用于显示器开始，它的研究才有了前所未有的动力。在这最近的几十年时间里液晶显示器有了长足的进步，目前液晶显示器已是整个领域中的佼佼者，只要稍加留意，不难发现市场上用液晶显示器的仪器仪表、计算器、计算机、彩色电视机等不仅品种越来越多，而且显示品质亦越来越高，价格越来越便宜。目前，各种形态的液晶材料基本上都用于开发液晶显示器，现在已开发出的各种向列相液晶、聚合物分散液晶、双（多）稳态液晶、铁电液晶和反铁电液晶显示器等。而在液晶显示中，开发最成功、市场占有量最大、发展最快的是向列相液晶显示器。按照液晶显示模式，常见向列相显示就有T N（扭曲向列相）模式，H T N（高扭曲向列相）模式、S T N（超扭曲向列相）模式、T F T（薄膜晶体管）模式等。其中TFT模式是近10年发展最快的显示模式。
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