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61b) An airplane of mass 70 000 kg is traveling due north at latitude 30◦ north, at an altitude of 10 km (32 800 ft) with a speed of 300 m/s (671 mph). Calculate (a) the components of the absolute velocity and acceleration along the axes of the topocentric-horizon reference frame, and (b) the net force on the airplane. 4 m/s (901 mph) component of velocity to the east (x direction) is due entirely to the earth’s rotation. 02187 m/s2 is the Coriolis acceleration. 12 shows the components of this relatively small force.

Keep in mind that O remains directly xyz frame are ˆiˆjk, below P, so that as P moves, so do the xyz axes. Thus, the ˆiˆjkˆ triad, which are the unit vectors of a spherical coordinate system, vary in direction as P changes location, thereby accounting for the curvature of the earth. Let us find the absolute velocity and acceleration of P. 42 to calculate their inertial values. , its altitude). 24. 51) The acceleration of P relative to the non-rotating earth is found by taking the time derivative of vrel .

15, leads to six constants of integration. In this section it would seem that we have arrived at those constants, namely the three components of the angular momentum h and the three components of the eccentricity vector e. However, we showed that h is perpendicular to e. This places a condition, namely h · e = 0, on the components of h and e, so that we really have just five independent constants of integration. The sixth constant of the motion will arise when we work time back into the picture in the next chapter.

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A Comparison of Certain Electrical Properties of Ordinary and Uranium Lead (1919)(en)(3s) by Percy Williams Bridgman


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