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generally accepted performance grades used for gyroscopes, based on their intended applications but not necessarily including integrated GPS=INS applications These are only rough order-of-magnitude ranges for the different error characteristics Sensor requirements are largely determined by the application For example, gyroscopes for gimbaled systems generally require smaller input ranges than those for strapdown applications 6233 Sensor Types Gyroscope designers have used many different approaches to a common sensing problem, as evidenced by the following samples There are many more, and probably more yet to be discovered Momentum Wheels Momentum wheel gyroscopes use a spinning mass patterned after the familiar child's toy gyroscope.

If the spinning momentum wheel is mounted inside gimbals to isolate it from rotations of the body on which it is mounted, then its spin axis tends to remain in an inertially xed direction and the gimbal angles provide a readout of the total angular displacement of that direction from body- xed axis directions If, instead, its spin axis is torqued to follow the body axes, then the required torque components provide a measure of the body angular rates normal to the wheel spin axis In either case, this type of gyroscope can potentially measure two components (orthogonal to the momentum wheel axle) of angular displacement or rate, in which case it is called a two-axis gyroscope Because the drift characteristics of momentum wheel gyroscopes are so strongly affected by bearing torques, these gyroscopes are often designed with innovative bearing technologies (eg, gas, magnetic, or electrostatic bearings).

, the patient s path may have been 1 2 3 4, but another possibility is 1 2 3 2 1 2 3 4 Furthermore, the patient s path may be subject to censoring Although censored data is incomplete in that the nal transition is not observed to occur, when dealing with owgraphs we make the distinction between censored data and what we will refer to as incomplete data The term complete data refers to complete transition information and includes right-censored observations For example, in Section 73, the retinopathy data had many right-censored observations If an observation were censored in state 2, the implicit assumption is that the person could transit to either state 1 or state 3, as both states are connected by direct branches from state 2, and hence the transition information is complete although the waiting time is censored De nition 801.

If the mechanical coupling between the momentum wheel and its axle is exible with just the right mechanical spring rate depending on the rotation rate and angular momentum of the wheel the effective torsional spring rate on the momentum wheel can be canceled This type of dynamical ``tuning'' isolates the gyroscope from bearing torques and generally improves gyroscope performance Coriolis Effect The Coriolis effect is named after Gustave Gaspard de Coriolis (1792 1843), who described the apparent acceleration acting on a body moving with constant velocity in a rotating coordinate frame [26] It can be modeled in terms of the vector cross-product (de ned in Section B2.

10) as aCoriolis O v P Q P Q v1 O1 T U T U T O2 U T v2 U R S R S O3 v3 P Q O2 v3 O3 v2 T U T O3 v1 O1 v3 U; R S O1 v2 O2 v1 6:7 6:8.

Incomplete data consists of data that have complete information on observed waiting times but incomplete information on the associated transitions The contribution of the censored observation is a nite mixture distribution weighted by the respective transition probabilities The main problem when dealing with incomplete data having missing transitions is the dif culty in calculating the contribution of the incomplete data terms to the likelihood In this chapter.

******** STACK TOP ********** rule r3 Time Tags 9 8 4 pconf 0 ******** STACK BOTTOM ********** >> Use any other debugging commands that might help illuminate the ow of the program 126 RULES THAT MAKE THEMSELVES REFIREABLE: RUNAWAY PROGRAMS AND RECURSION Rules can make themselves re reable very simply; by modifying an antecedent datum so that the modi ed data still satisfy the antecedent This can be the source of an annoying bug causing a runaway program, or can be the basis of a powerful technique, recursion In recursion, the same rule or rules re over and over again with something different each time they re until some criterion is met that terminates the process We have two example programs to illustrate recursion, but will not go into them in any detail; the student may run and explore them at will Program LOGIST.