We have seen that the work done by a force F on a particle is given by dw =. dr. If the work done by F, when the particle moves from any position TI to any position T2, can be expressed as, W12=fdr=-(V(r2)-V(1)=V-v2, (1) then we say that the force is conservative. In the above expression, the scalar

In this lecture we will look at some applications of Newton's second law, expressed in the different coordinate systems that were introduced in lectures D3-D5. Recall that Newton's second law F=ma, (1) is a vector equation which is valid for inertial observers. In general, we will be interested in determining the motion of a particle given

In lecture D2 we introduced the position velocity and acceleration vectors and referred them to a fixed cartesian coordinate system. While it is clear that the choice of coordinate system does not affect the final answer, we shall see that, in practical problems, the choice of a specific system may simplify the calculations considerably. In previous lectures, all the vectors at all points in the trajectory were expressed in the

In this lecture we will look at some other common systems of coordinates. We will present polar coordinates in two dimensions and cylindrical and spherical coordinates in three dimensions. We shall see that these systems are particularly useful for certain classes of problems Like in the case of intrinsic coordinates presented in the previous lecture, the reference frame changes from point to point. However, for the coordinate systems to be presented below, the reference frame depends only on the position of the particle. This is in contrast with the intrinsic coordinates, where the reference frame is a function of the position, as well as the path

is a vector equation that relates the magnitude and direction of the force vector, to the magnitude and direction of the acceleration vector. In the previous lecture we derived expressions for the acceleration vector expressed in cartesian coordinates. This expressions can now be used in Newton's second law, to produce the equations of motion expressed in cartesian coordinates

支付已知现金收益资产远期合约的定价 无收益资产远期合约的定价 远期价格与期货价格 远期(期货)价格与标的资产现货价格的关系 支付已知收益率资产远期合约的定价 远期与期货价格的一般结论

We will start by studying the motion of a particle. We think of particle as a body which has mass, but has negligible dimensions. Treating bodies as particles is, of course, an idealization which involves an approximation. This approximation may be perfectly acceptable in some situations and not adequate in some other cases. For instance, if we want to study the motion of planets it is common to consider each planet as a particle

In this course we will study Classical Mechanics. Particle motion in Classical Mechanics is governed by Newton's laws and is sometimes referred to as Newtonian Mechanics. These laws are empirical in that they combine observations from nature and some intuitive concepts. Newton's laws of motion are not self evident. For instance, in Aristotelian mechanics before Newton, force was thought to be required in order

第一节机床的分类、型号编制方法和构造 第二节车床与车刀 第三节钻床、镗床与孔加工刀具 第四节铣床与铣刀 第五节刨床、拉床及工艺特点 第六节磨床与砂轮 第七节齿轮加工机床与齿轮加工刀具

第一节基本概念 第二节定位基准的选择 第三节工艺路线的拟定 第四节加工余量及工序间尺寸的确定 第五节工艺尺寸链的计算 第六节时间定额及劳动生产率 第七节典型零件工艺