Previous studies of precariously balanced objects in seismically active regions provide important information for aseismatic engineering and theoretical seismology. They are almost founded on an oversimplified assumption: any 3-dimensional (3D) actual object with special symmetry could be regarded as a 2D finite object in light of the corresponding symmetry. To gain an actual evolution of precariously balanced objects subjected to various levels of ground accelerations, a 3D investigation should be performed. In virtue of some reasonable works from a number of mechanicians, we derive three resultant second-order ordinary differential equations determine the evolution of 3D responses. The new dynamic analysis is following the 3D rotation of a rigid body around a fixed point. A computer program for numerical solution of these equations is also developed to simulate the rocking and rolling response of axisymmetric objects to various levels of ground accelerations. It is shown that the 2D and 3D estimates on the minimum overturning acceleration of a cylinder under the same sets of half- and full-sine-wave pulses are almost consistent except at several frequency bonds. However, we find that the 2D and 3D responses using the actual seismic excitation have distinct differences, especially to north-south (NS) and up-down (UD) components. In this work the chosen seismic wave is the El Centro recording of the 18 May 1940 Imperial Valley Earthquake. The 3D outcome does not seem to support the 2D previous result that the vertical component of the ground acceleration is less important than the horizontal ones. We conclude that the 2D dynamic modeling is not always reliable.
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