1. Date of download: 6/21/2016 Copyright © ASME. All rights reserved. From: Study of the Apsidal Precession of the Physical Symmetrical Pendulum J. Appl. Mech. 2015;82(2):021008-021008-12. doi:10.1115/1.4029470 Inertial system XYZ and the spherical pendulum. The angular coordinates θ and ϕ are shown, as well as the weight and tension. Figure Legend:

2. Date of download: 6/21/2016 Copyright © ASME. All rights reserved. From: Study of the Apsidal Precession of the Physical Symmetrical Pendulum J. Appl. Mech. 2015;82(2):021008-021008-12. doi:10.1115/1.4029470 (a) Graphical form of the approximate and exact solutions (dashed and solid lines, respectively) of the ISP for θ with 300 ≤ τ ≤ 310. These graphics cannot be distinguished from each other. (b) Graphical form of the approximate values of the angle ϕ coming from Eq. (40) and the exact values (dashed and solid lines, respectively), for 500 ≤ τ ≤ 510. The approximate and exact solutions are superposed. In addition, the straight line corresponds to the linear approximation given by Eq. (43). Figure Legend:

3. Date of download: 6/21/2016 Copyright © ASME. All rights reserved. From: Study of the Apsidal Precession of the Physical Symmetrical Pendulum J. Appl. Mech. 2015;82(2):021008-021008-12. doi:10.1115/1.4029470 Projection of the trajectory of the ISP on the XY plane for 30nT ≤ t ≤ (30n + 1)T with n = 0, 1, and 2, using the approximate solution (47) and the exact one (dashed and solid lines, respectively). The approximate and exact solutions cannot be distinguished. Figure Legend:

4. Date of download: 6/21/2016 Copyright © ASME. All rights reserved. From: Study of the Apsidal Precession of the Physical Symmetrical Pendulum J. Appl. Mech. 2015;82(2):021008-021008-12. doi:10.1115/1.4029470 PSP hung on an edge. θ, Φ, and ψ are the Euler angles used in the description of the motion. The spherical coordinate ϕ is shown as well as its relation with the Euler angle Φ. Figure Legend:

5. Date of download: 6/21/2016 Copyright © ASME. All rights reserved. From: Study of the Apsidal Precession of the Physical Symmetrical Pendulum J. Appl. Mech. 2015;82(2):021008-021008-12. doi:10.1115/1.4029470 Plot of the approximate solution (88) and the exact one (dashed and solid lines, respectively) for the coordinate of nutation θ¯(sinθ) of the PSP as a function of time, for 500 ≤ t ≤ 504 s. The exact solution is superposed to the approximate one. Figure Legend:

6. Date of download: 6/21/2016 Copyright © ASME. All rights reserved. From: Study of the Apsidal Precession of the Physical Symmetrical Pendulum J. Appl. Mech. 2015;82(2):021008-021008-12. doi:10.1115/1.4029470 (a) Approximate and exact solutions (dashed and solid lines, respectively) for the azimuthal angle Φ of the PSP, for 500 ≤ t ≤ 504 s, (b) approximate and exact solutions (dashed and solid lines, respectively) for the spin angle ψ of the PSP, for 500 ≤ t ≤ 504 s. The straight lines correspond to the linear approximations for each one of these angles. The exact solutions cannot be distinguished from the approximate ones. Figure Legend:

7. Date of download: 6/21/2016 Copyright © ASME. All rights reserved. From: Study of the Apsidal Precession of the Physical Symmetrical Pendulum J. Appl. Mech. 2015;82(2):021008-021008-12. doi:10.1115/1.4029470 Projections of the trajectory of the CM of the PSP on the XY plane, obtained with the approximate and exact solutions (dashed and solid lines, respectively), for time intervals of a period T, (a) for 0 ≤ t ≤ T: (T). (b) For 29 T ≤ t ≤ 30 T: (30 T). (c) for 59 T ≤ t ≤ 60 T: (60 T). In all cases, the exact solutions are superposed to the approximate ones. Figure Legend: