In this lecture, we will revisit the application of Newton's second law to a system of particles and derive some useful relationships expressing the conservation of angular momentum. Center of Mass Consider a system made up of n particles. A typical particle, i, has mass mi, and, at the instant considered, occupies the position Ti relative to a frame xyz. We can then define the center of mass, G, as the point
n contrast to alcohols with their rich chemical reactivity, ethers (compounds contain- ing a C-0-C unit) undergo relatively few chemical reactions. As you saw wher we discussed Grignard reagents in Chapter 14 and lithium aluminum hydride reduc- tions in Chapter 15, this lack of reactivity of ethers makes them valuable as solvents in a number of synthetically important transformatio. In the present chapter you will learn
H ydrocarbons that contain carbon-carbon triple bond are called alkynes. Non- cyclic alkynes have the molecular formula C, H2n-2. Acetylene (HCCH) is th simplest alkyne. We call compounds that have their triple bond at the end of a carbon chain(RC=CH) monosubstituted, or terminal, alkynes. Disubstituted alkynes (RCCR') are said to have internal triple bonds. You will see in this chapter that a car- bon-carbon triple bond is a functional group, reacting with many of the same reagents
Shock Capturing vs. Shock Fitting hocks when the shocks or di n the solution as regions of large gradients without having to give them any special treatment. If we use conservative schemes, the Lax-Wendroff theorem 's. will be to a weak solution We know tha reak solutions satisfy the jump conditions and therefore give the correct shock
微元法 我们先回忆一下求曲边梯形面积S 的步骤：对区间[, ] a b 作划分 ax x x x b = 012 < < <\< n = ， 然后在小区间 ],[ 1 ii xx − 中任取点ξ i ，并记 =Δ − iii −1 xxx ，这样就得到了小 曲边梯形面积的近似值 i ii Δ ≈ ξ )( ΔxfS 。最后，将所有的小曲边梯形面积 的近似值相加，再取极限，就得到
Stability Condition in Terms of the Pole Locations A causal LTI digital filter is BIBO stable if and only if its impulse response h[n] is absolutely summable, i.e., We now develop a stability condition in terms of the pole locations of the transfer function H(z)
