By S. (ed) Flugge

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**Extra info for Continuum mechanics IV: Problems of non-linear elasticity**

**Sample text**

In general lhe harmonics have along half a parallel. m(cos9) cosm~ (m = 1, 2, . m(cos9) sinm~ (m = 1, 2, . ). 13) 34 CHAPTER 2 is more commonly used. 14 ) , when compared with eq. 18) is real. 2. 20') With the introduction of its mass M and mean radius R we have made the coefficients Vg,m dimensionless and set Vo 0 = 1, fixing the ratio THE GRAVITATIONAL FIELD OF A PLANET 35 GM/R. 20). Each Il. corresponds to a different kind of deviation from spherical symmetry, the larger Il. g1Vmg rise to a smaller gravitational field at great distances: the gravitational field corresponding to the order Il.

3. Calculate the potential perturbation and the gravity anomaly on a flat earth due to (i) a uniform sphere and (ii) a uniform infinite cylinder buried under the surface and with a different density. Hint: use Gauss' theorem. 4. Estimate the velocity change of a spacecraft in a low orbit flying across a mountain range. Hint: model the range as a cylinder placed on the surface of a flat earth. 5. Calculate the spherical harmonics of order 3. From Y30 find the north-south asymmetry of the profile of the geoid on a meridian.

1) obtained with a nominal earth rotation frequency 0)0. The units of time and distance so defined are independent. By transferring the frequency standard from the microwave to the optical THE ROTATION OF THE EARTH AND OTHER PLANETS 47 band it is possible to measure the frequency of the line whose wavelength determines the standard of length and therefore to determine their product, the velocity of light, with the dimensions crn/s. This transfer over a frequency range of about 10 decades, however, is subject to errors; moreover, the stability of the lasers used in interferometric techniques is much less than the stability of atomic frequency standards.

### Continuum mechanics IV: Problems of non-linear elasticity by S. (ed) Flugge

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