Generalization of parallel axis theorem for rotational inertia

Abdulghany, A. R.

doi:10.1119/1.4994835

Cited by 23 publications

(10 citation statements)

References 10 publications

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“…In this paper, we have employed Dirac's bra-ket notation [9][10][11] to define the inertia tensor operator I in Eq. (8). This operator is independent of the choice of bases or coordinate system.…”

Section: Discussionmentioning

confidence: 99%

Bra-Ket Representation of the Inertia Tensor

Kim

Lee

2020

J. Korean Phys. Soc.

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We employ Dirac's bra-ket notation to define the inertia tensor operator that is independent of the choice of bases or coordinate system. The principal axes and the corresponding principal values for the elliptic plate are determined only based on the geometry. By making use of a general symmetric tensor operator, we develop a method of diagonalization that is convenient and intuitive in determining the eigenvector. We demonstrate that the bra-ket approach greatly simplifies the computation of the inertia tensor with an example of an N-dimensional ellipsoid. The exploitation of the bra-ket notation to compute the inertia tensor in classical mechanics should provide undergraduate students with a strong background necessary to deal with abstract quantum mechanical problems.

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Section: Discussionmentioning

confidence: 99%

Bra-Ket Representation of the Inertia Tensor

Kim

Lee

2020

J. Korean Phys. Soc.

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“…After software analysis and calculation, the quality of support frame and mirror is about 0.461 kg during elevating rotation, moment of inertia is 0:000513 kg•m 2 . According to the parallel axis theorem of inertia [21],…”

Section: Design Calculation and Selection Of Key Componentsmentioning

confidence: 99%

Single Reflect-Mirror Laser Communication Tracking-Pointing System Load Technology for Micronanosatellite

Chi

Zhang

Meng

2022

Advances in Mathematical Physics

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In order to realize low-orbit microsatellite laser communication, L- and U-frame structures are designed, respectively, for the payload of single-lens reflex (SLR) laser communication tracking and pointing system. According to the characteristics of each load structure, the detailed system design is carried out, and the modal analysis is carried out on the key structural parts of the L- and U-frames to ensure the reliability of each load structure. The pointing accuracy of the two load structures is also calculated and analyzed. Finally, the conclusion is that both of the two load structures can meet the technical and accuracy requirements of low-orbit communication, but obviously, the U-frame structure has higher accuracy, greater pitching angle, and better reliability; eventually, the U-frame structure is adopted in this design. Then, we have completed the manufacture and assembly of the principle prototype and carried out a vibration test experiment on the principle prototype. The results show that the U-type loading structure SLR laser communication tracking and pointing system achieves the expected design purpose and can meet the technical requirements of the low-orbit microsatellite laser communication.

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“…In the latter case, extra care must be taken, as both centres of inertia must be in the same coordinate system before the summation can be performed. This can be easily performed by means of the parallel axis theorem [HV28, Abd17], and translating both moments of inertia to the axis that goes though the total centre of mass

C_{T}

. Note that this is trivial for the graph, but the calculation for the submerged object is a bit more involved (see Figure 8).…”

Section: Hollow/permeable Objectsmentioning

confidence: 99%

Realistic Buoyancy Model for Real‐Time Applications

Bajo

Patow

Delrieux

2020

Computer Graphics Forum

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Following Archimedes' Principle, any object immersed in a fluid is subject to an upward buoyancy force equal to the weight of the fluid displaced by the object. This simple description is the origin of a set of effects that are ubiquitous in nature, and are becoming commonplace in games, simulators and interactive animations. Although there are solutions to the fluid‐to‐solid coupling problem in some particular cases, to the best of our knowledge, comprehensive and accurate computational buoyancy models adequate in general contexts are still lacking. We propose a real‐time Graphics Processing Unit (GPU) based algorithm for realistic computation of the fluid‐to‐solid coupling problem, which is adequate for a wide generality of cases (solid or hollow objects, with permeable or leak‐proof surfaces, and with variable masses). The method incorporates the behaviour of the fluid into which the object is immersed, and decouples the computation of the physical parameters involved in the buoyancy force of the empty object from the mass of contained liquid. The dynamics of this mass of liquid are also computed, in a way such that the relation between the centre of mass of the object and the buoyancy force may vary, leading to complex, realistic beha viours such as the ones arising for instance with a sinking boat.

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Generalization of parallel axis theorem for rotational inertia

Cited by 23 publications

References 10 publications

Bra-Ket Representation of the Inertia Tensor

Bra-Ket Representation of the Inertia Tensor

Single Reflect-Mirror Laser Communication Tracking-Pointing System Load Technology for Micronanosatellite

Realistic Buoyancy Model for Real‐Time Applications

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