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Before Einstein s time, physicists determined that light has wavelike properties and in some ways resembles sound However, light travels much faster than sound Also, light can propagate through a vacuum, whereas sound cannot Sound waves require a material medium such as air, water, or metal to get from one place to another Many scientists suspected that light also must need some sort of medium to travel through space What could exist everywhere, even between the stars and galaxies, and even in a jar from which all the air was pumped out This mysterious medium was called luminiferous ether, or simply ether If the ether exists, some scientists wondered, how could it pass right through everything, even the entire Earth, and get inside an evacuated chamber How could the ether be detected One idea was to see if the ether blows against the Earth as our planet orbits around the Sun, as the Solar System orbits around the center of the Milky Way galaxy, and as our galaxy drifts through the Cosmos If there is an ether wind, then the speed of light ought to be different in different directions This, it was reasoned, should occur for the same reason that a passenger on a fast-moving truck measures the speed of sound waves coming from the front as faster than the speed of sound waves coming from behind In 1887, an experiment was done by two physicists named Albert Michelson and Edward Morley in an attempt to find out how fast the ether wind is blowing and from what direction The Michelson-Morley experiment, as it became known, showed that the speed of light is the same in all directions This cast doubt on the ether theory If the ether exists, then according to the results obtained by Michelson and Morley, it must be moving right along with the Earth This is quite a coincidence; it implies that the Earth is stationary relative to absolute space, and no one believed that in 1887 Attempts were made to explain away this result by suggesting that the Earth drags the ether along with itself Einstein could not believe this He decided that the results of the Michelson-Morley experiment had to be taken at face value: The speed of light is constant in every direction Einstein believed that the MichelsonMorley experiment would have the same outcome for observers on the Moon, on any other planet, on a space ship, or anywhere in the Universe.

The term PRn ( b b )Rb has been dropped as it is second order in ib in n b the error quantities In eqn (1049), P = [ ]; therefore, the equation

FIGURE 15-26

contains only three independent terms Using eqns (223) and (B15), eqn (1049) can be written in the vector form, = Rn ( b b ) b ib in (1050)

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Another efficient way to create relationships is to use the Diagram tab of the Project window With the Diagram tab selected, you will notice a set of buttons, shown in Figure 15-26, that appear in the toolbar The rightmost button is used for defining relationships in the diagram You can also use this toolbar to create folders, namespaces, and query subjects, but the relative convenience of the buttons for those objects is nowhere near that of the relationship button Clicking the relationship button will change the cursor to indicate that it is ready to create a relationship You can then drag-and-drop from one query subject to another in the diagram to establish the relationship Doing so will also bring up the Relationship Definition dialog shown in Figure 15-27 Because the relationship was created using one of the efficient methods, Framework Manager created the link between the selected query items and gave a useful default name, using the names of the two query subjects separated by the string <--> to signify the relationship between them You can rename it if you wish, but you should stick with the names and the naming convention that these creation methods produce The components of the relationship are the two referenced query subjects, the link or links shown between the query subjects, the query items referenced by each link, and the

Einstein rejected the notion of luminiferous ether Instead, he proposed an axiom, a fundamental rule of the Universe: The speed at which light (and

where b is the error in the gyro measurement of the body-frame inertialib relative angular rate From eqn (257), the vector n is de ned as in n in ( + ie ) cos( ) = + ie ) sin( ) ( (1051)

Part IV:

ve v where = cos( )(RN +h) and = RMn Therefore, the vector b depends in +h on the error in position and velocity, which are not available to AHRS applications Further specialization of eqn (1050) is considered in Section 1142 in relation to INS applications The following section considers the special case relevant to AHRS applications

any other EM field) travels in a vacuum is the same no matter what the direction and regardless of the motion of the observer with respect to the EM energy source Then he set out to deduce what logically follows from this assumption Einstein did all his work by using a combination of mathematics and daydreaming that he called mind journeys He wasn t an experimentalist but a theorist There is a saying in physics: One experimentalist can keep a dozen theorists busy Einstein turned this inside out His theories have kept thousands of experimentalists occupied

FIGURE 15-27

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