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In Structure mode, each column heading will have the following cell contents by default:

18:

Similar to the trapezoidal acceleration curve, we use b = 1/8 in the derivation The equations of the curve from A to B are Displacement Velocity q 1 2q y = h sin 4p , b 2p b y =

Next, GenericsDemo declares an object of type Gen<string>:

=NameOf([Variable])

Gen<string> strOb = new Gen<string>("Generics add power");

h q 2 - 2 cos 4p , b b 8p h q Acceleration y = 2 sin 4p , b b where h = maximum rise for cycloidal segment When point B is reached, q =

Because the type argument is string, string is substituted for T inside Gen This creates a string version of Gen, as the remaining lines in the program demonstrate Before moving on, a few terms need to be defined When you specify a type argument such as int or string for Gen, you are creating what is referred to in C# as a closed constructed type Thus, Gen<int> is a closed constructed type In essence, a generic type, such as Gen<T>, is an abstraction It is only after a specific version, such as Gen<int>, has been constructed that a concrete type has been created In C# terminology, a construct such as Gen<T> is called an open constructed type, because the type parameter T (rather than an actual type, such as int) is specified More generally, C# defines the concepts of an open type and a closed type An open type is a type parameter or any generic type whose type argument is (or involves) a type parameter Any type that is not an open type is a closed type A constructed type is a generic type for which all type arguments have been supplied If those type arguments are all closed types, then it is a closed constructed type If one or more of those type arguments are open types, it is an open constructed type

=NameOf([Quarter])

A key point to understand about generic types is that a reference of one specific version of a generic type is not type-compatible with another version of the same generic type For example, assuming the program just shown, the following line of code is in error and will not compile:

(32)

iOb = strOb; // Wrong!

Each data row will have the following contents, where Variable is the universe object or report variable:

Even though both iOb and strOb are of type Gen<T>, they are references to different types because their type arguments differ

At this point, you might be asking yourself the following question Given that the same functionality found in the generic Gen class can be achieved without generics, by simply specifying object as the data type and employing the proper casts, what is the benefit of making Gen generic The answer is that generics automatically ensure the type safety of all operations involving Gen In the process, generics eliminate the need for you to use casts and type-check code by hand To understand the benefits of generics, first consider the following program that creates a non-generic equivalent of Gen:

=[Variable]

b Substituting this value of q into Eq (32) provides the 8 characteristic equations at point B 1 1 y1 = h 4 2p 2h y1 = b 8p h y1 = 2 b

// NonGen is functionally equivalent to Gen but does not use generics using System; class NonGen { object ob; // ob is now of type object // Pass the constructor a reference of type object public NonGen(object o) {

Part I:

=[Quarter]

The general expression for displacement under constant acceleration has a displacement 1 y = n 0q + aq 2 2 where n0 = follower initial velocity, dimensionless a = follower acceleration, dimensionless q = cam angle rotation, radians (224)