A Theoretical and Numerical Study of the Dzhanibekov and Tennis Racket Phenomena

2015 ◽  
Author(s):  
Hidenori Murakami ◽  
Oscar Rios ◽  
Thomas J. Impelluso
Keyword(s):  
Numerical Study ◽  
Space Station ◽  
The Body ◽  
Moving Frame ◽  
Coordinate Frame ◽  
Moments Of Inertia ◽  
Tennis Racket ◽  
Angular Momenta ◽  
Principal Axes ◽  
Moving Coordinate

In this paper, we present complete explanation of the Dzhanibekov phenomenon demonstrated in a space station (www.youtube.com/watch?v=L2o9eBl_Gzw) and the tennis racket phenomenon (www.youtube.com/watch?v=4dqCQqI-Gis). These phenomena are described by Euler’s equation of an unconstrained rigid body that has three distinct values of moments of inertia. In the two phenomena, the rotations of a body about the principal axes that correspond to the largest and the smallest moments of inertia are stable. However, the rotation about the axis corresponding to the intermediate principal moment of inertia becomes unstable, leading to the unexpected rotations that are the basis of the phenomena. If this unexpected rotation is not explained from a complete perspective which accounts for the relevant physical and mathematical aspects, one might misconstrue the phenomena as a violation of the conservation of angular momenta. To address this, especially for students, we investigate the phenomena using more precise mathematical and graphical tools than those employed previously. Following Élie Cartan [1], we explicitly write the vector basis of a body-attached, moving coordinate system. Using this moving frame method, we describe the Newton and Euler equations. The adoption of the moving coordinate frame expresses the rotation of the body more clearly and allows us to use the Lie group theory of special orthogonal group SO(3). We integrate the torque-free Euler equation using the fourth-order Runge-Kutta method. Then we apply a recovery equation to obtain the rotation matrix for the body. By combining the geometrical solutions with numerical simulations, we demonstrate that the unexpected rotations observed in the Dzhanibekov and the tennis racket experiments preserve the conservation of angular momentum.

A Theoretical and Numerical Study of the Dzhanibekov and Tennis Racket Phenomena1

2016 ◽  
Vol 83 (11) ◽  
Author(s):  
Hidenori Murakami ◽  
Oscar Rios ◽  
Thomas Joseph Impelluso
Keyword(s):  
Angular Momentum ◽  
Numerical Study ◽  
The Body ◽  
Moment Of Inertia ◽  
Kutta Method ◽  
Principal Moment ◽  
Tennis Racket ◽  
Angular Momenta ◽  
Runge Kutta Method ◽  
Principal Axes

This paper presents a complete explanation of the Dzhanibekov and the tennis racket phenomena. These phenomena are described by Euler's equation for an unconstrained rigid body that has three distinct moment of inertia values. In the two phenomena, the rotations of a body about the principal axes that correspond to the largest and the smallest moments of inertia are stable. However, the rotation about the axis corresponding to the intermediate principal moment of inertia becomes unstable, leading to the unexpected rotations that are the basis of the phenomena. If this unexpected rotation is not explained from a complete perspective which accounts for the relevant physical and mathematical aspects, one might misconstrue the phenomena as a violation of the conservation of angular momenta. To address this, the phenomenon is investigated using more precise mathematical and graphical tools than those employed previously. The torque-free Euler equations are integrated using the fourth-order Runge–Kutta method. Then, a recovery equation is applied to obtain the rotation matrix for the body. By combining the geometrical solutions with numerical simulations, the unexpected rotations observed in the Dzhanibekov and the tennis racket experiments are shown to preserve the conservation of angular momentum.

Spin Rotor Stabilization of a Dual-Spin Spacecraft with Time Dependent Moments of Inertia

1998 ◽  
Vol 08 (03) ◽  
pp. 609-617 ◽  
Author(s):  
V. Lanchares ◽  
M. Iñarrea ◽  
J. P. Salas
Keyword(s):  
Periodic Function ◽  
Center Of Mass ◽  
The Body ◽  
Body Motion ◽  
Time Dependent ◽  
Moments Of Inertia ◽  
Melnikov's Method ◽  
Melnikov’S Method ◽  
Principal Axes

We consider a dual-spin deformable spacecraft, in the sense that one of the moments of inertia is a periodic function of time such that the center of mass is not altered. In the absence of external torques and spin rotors, by means of the Melnikov's method we prove that the body motion is chaotic. Stabilization is obtained by means of a spinning rotor about one of the principal axes of inertia.

REPEATED LONG-TERM SPACE FLIGHTS: PROTEOMIC INVESTIGATIONS OF COSMONAUTS' BLOOD

2020 ◽  
Vol 54 (5) ◽  
pp. 15-22
Author(s):  
I.M. Larina ◽  
◽  
D.N. Kashirina ◽  
K.S. Kireev ◽  
A.I. Grigoriev ◽  
...  
Keyword(s):  
Bone Structure ◽  
Space Station ◽  
The Body ◽  
Coagulation Cascade ◽  
Chemical Components ◽  
Blood Proteins ◽  
Blood Indices ◽  
Before And After ◽  
Biochemical Indices

We performed the first ever comparative analysis of modifications in the proteome, ionogram and some other blood plasma biochemical indices of 18 male cosmonauts (44 ± 6 years of age) before and after maiden or repeated long-term missions to the Russian segment of the International space station (ISS RS). Levels of proteins, substrates and ions as well as chemical components were measured using the LC-MS-based proteomics and routine biochemical techniques. A total of 256 to 281 indices were investigated with the methods of descriptive statistic, regression analysis, and access to bioinformatics resources. It was shown that blood indices recovery from the maiden and repeated missions reflects changes in the body systems and goes at a various speed. The results of measurements made prior to launch and on day 7 after landing are dependent on the number of missions. The bioinformatics techniques showed that after maiden missions both the mediator proteins of alkaline phosphatase (AP) and blood proteins with reliably changing concentrations are associated with the bio-processes including stress, metabolism and DNA reparation, apoptosis, catabolism and proteolysis. During early re-adaptation from repeated missions the AP level was affected by bone remodeling, phosphorylation, angiogenesis and coagulation cascade suggesting a distinct and urgent trigger of the processes of bone structure and mineralization.

scholarly journals Method for assessment of matching of total ankle joint endoprostheses based on CT data

2020 ◽  
Vol 6 (3) ◽  
pp. 396-397
Author(s):  
Heiner Martin ◽  
Josephine Wittmüß ◽  
Thomas Mittlmeier ◽  
Niels Grabow
Keyword(s):  
Cross Sections ◽  
Spline Functions ◽  
Moments Of Inertia ◽  
Cad System ◽  
Principal Moments Of Inertia ◽  
Principal Axes ◽  
Ct Data ◽  
The One ◽  
Relative Differences ◽  
Systemic Design

AbstractThe investigation of matching of endoprosthesis tibial components to the bone cross section is of interest for the manufacturer as well as for the surgeon. On the one hand, a systemic design of the prosthesis and the assortment is possible, on the other hand, a better matching implantation is enabled on the basis of experience of this study. CT sections were segmented manually using a CAD system and fitted by spline functions, then superseded with cross sections of the tibial component of a modified Hintermann H3 prosthesis. The principal moments of inertia, the direction of the principal axes and the area of the section were evaluated. Based on the relative differences of the principal moments of inertia, recommendations for application of the different prosthesis size and its selection with the surgery can be made.

scholarly journals A Computational Study on the Role of Parameters for Identification of Thyroid Nodules by Infrared Images (and Comparison with Real Data)

Sensors ◽  
2021 ◽  
Vol 21 (13) ◽  
pp. 4459
Author(s):  
José R. González ◽  
Charbel Damião ◽  
Maira Moran ◽  
Cristina A. Pantaleão ◽  
Rubens A. Cruz ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Thyroid Nodules ◽  
Numerical Study ◽  
Computational Study ◽  
Internal Heat ◽  
Heat Transfer Process ◽  
The Body ◽  
Physical Parameters ◽  
Infrared Sensors ◽  
Wide Range

According to experts and medical literature, healthy thyroids and thyroids containing benign nodules tend to be less inflamed and less active than those with malignant nodules. It seems to be a consensus that malignant nodules have more blood veins and more blood circulation. This may be related to the maintenance of the nodule’s heat at a higher level compared with neighboring tissues. If the internal heat modifies the skin radiation, then it could be detected by infrared sensors. The goal of this work is the investigation of the factors that allow this detection, and the possible relation with any pattern referent to nodule malignancy. We aim to consider a wide range of factors, so a great number of numerical simulations of the heat transfer in the region under analysis, based on the Finite Element method, are performed to study the influence of each nodule and patient characteristics on the infrared sensor acquisition. To do so, the protocol for infrared thyroid examination used in our university’s hospital is simulated in the numerical study. This protocol presents two phases. In the first one, the body under observation is in steady state. In the second one, it is submitted to thermal stress (transient state). Both are simulated in order to verify if it is possible (by infrared sensors) to identify different behavior referent to malignant nodules. Moreover, when the simulation indicates possible important aspects, patients with and without similar characteristics are examined to confirm such influences. The results show that the tissues between skin and thyroid, as well as the nodule size, have an influence on superficial temperatures. Other thermal parameters of thyroid nodules show little influence on surface infrared emissions, for instance, those related to the vascularization of the nodule. All details of the physical parameters used in the simulations, characteristics of the real nodules and thermal examinations are publicly available, allowing these simulations to be compared with other types of heat transfer solutions and infrared examination protocols. Among the main contributions of this work, we highlight the simulation of the possible range of parameters, and definition of the simulation approach for mapping the used infrared protocol, promoting the investigation of a possible relation between the heat transfer process and the data obtained by infrared acquisitions.

A NUMERICAL STUDY ON THE HEMODYNAMIC AND SHEAR STRESS OF DOUBLE ANEURYSM THROUGH S-SHAPED VESSEL

2015 ◽  
Vol 27 (04) ◽  
pp. 1550033 ◽  
Author(s):  
Mahdi Halabian ◽  
Alireza Karimi ◽  
Borhan Beigzadeh ◽  
Mahdi Navidbakhsh
Keyword(s):  
Blood Flow ◽  
Mechanical Behavior ◽  
Numerical Study ◽  
Flow Characteristics ◽  
Flow Simulation ◽  
The Body ◽  
Sweep Angle ◽  
Abdominal Aortic ◽  
Hemodynamic Characteristics ◽  
Refined Meshes

Abdominal aortic aneurysm (AAA) is a degenerative disease defined as the abnormal ballooning of the abdominal aorta (AA) wall which is usually caused by atherosclerosis. The aneurysm grows larger and eventually ruptures if it is not diagnosed and treated. Aneurysms occur mostly in the aorta, the main artery of the chest and abdomen. The aorta carries blood flow from the heart to all parts of the body, including the vital organs, the legs, and feet. The objective of the present study is to investigate the combined effects of aneurysm and curvature on flow characteristics in S-shaped bends with sweep angle of 90° at Reynolds number of 900. The fluid mechanics of blood flow in a curved artery with abnormal aortic is studied through a mathematical analysis and employing Cosmos flow simulation. Blood is modeled as an incompressible non-Newtonian fluid and the flow is assumed to be steady and laminar. Hemodynamic characteristics are analyzed. Grid independence is tested on three successively refined meshes. It is observed that the abrupt expansion induced by AAA results in an immensely disturbed regime. The results may have implications not only for understanding the mechanical behavior of the blood flow inside an aneurysm artery but also for investigating the mechanical behavior of the blood flow in different arterial diseases, such as atherosclerosis.

scholarly journals Electrochemotherapy Effectiveness Loss due to Electric Field Indentation between Needle Electrodes: A Numerical Study

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
José Alvim Berkenbrock ◽  
Rafaela Grecco Machado ◽  
Daniela Ota Hisayasu Suzuki
Keyword(s):  
Electric Field ◽  
In Silico ◽  
Treatment Effectiveness ◽  
Numerical Study ◽  
Specific Treatment ◽  
The Body ◽  
Membrane Selectivity ◽  
Chemotherapy Drugs ◽  
Mast Cell Tumor ◽  
Anticancer Treatment

Electrochemotherapy is an anticancer treatment based on applying electric field pulses that reduce cell membrane selectivity, allowing chemotherapy drugs to enter the cells. In parallel to electrochemotherapy clinical tests, in silico experiments have helped scientists and clinicians to understand the electric field distribution through anatomically complex regions of the body. In particular, these in silico experiments allow clinicians to predict problems that may arise in treatment effectiveness. The current work presents a metastatic case of a mast cell tumor in a dog. In this specific treatment planning study, we show that using needle electrodes has a possible pitfall. The macroscopic consequence of the electroporation was assessed through a mathematical model of tissue electrical conductivity. Considering the electrical and geometrical characteristics of the case under study, we modeled an ellipsoidal tumor. Initial simulations were based on the European Standard Operating Procedures for electrochemotherapy suggestions, and then different electrodes’ arrangements were evaluated. To avoid blind spots, multiple applications are usually required for large tumors, demanding electrode repositioning. An effective treatment electroporates all the tumor cells. Partially and slightly overlapping the areas increases the session’s duration but also likely increases the treatment’s effectiveness. It is worth noting that for a single application, the needles should not be placed close to the tumor’s borders because effectiveness is highly likely to be lost.

The Global Motion of a Rigid Body Subject to Periodic Body-Fixed Torques

1995 ◽  
Author(s):  
X. Tong ◽  
B. Tabarrok
Keyword(s):  
Rigid Body ◽  
Equations Of Motion ◽  
Melnikov Method ◽  
The Body ◽  
Body Motion ◽  
Heteroclinic Orbits ◽  
Coordinate Frame ◽  
Global Motion ◽  
Stable And Unstable Manifolds ◽  
Body Subject

Abstract In this paper the global motion of a rigid body subject to small periodic torques, which has a fixed direction in the body-fixed coordinate frame, is investigated by means of Melnikov’s method. Deprit’s variables are introduced to transform the equations of motion into a form describing a slowly varying oscillator. Then the Melnikov method developed for the slowly varying oscillator is used to predict the transversal intersections of stable and unstable manifolds for the perturbed rigid body motion. It is shown that there exist transversal intersections of heteroclinic orbits for certain ranges of parameter values.

Anthropometric Changes in Spaceflight

2021 ◽  
pp. 001872082110490
Author(s):  
Karen S. Young ◽  
K. Han Kim ◽  
Sudhakar Rajulu
Keyword(s):  
Body Shape ◽  
Space Station ◽  
The Body ◽  
Anthropometric Measurements ◽  
Space Suit ◽  
Anthropometric Data ◽  
Linear Measurements ◽  
Flight Phase ◽  
Overall Design ◽  
Shape Changes

Objective This study aims to identify the change in anthropometric measurements during spaceflight due to microgravity exposure. Background Comprehensive and accurate anthropometric measurements are crucial to assess body shape and size changes in microgravity. However, only limited anthropometric data have been available from the astronauts in spaceflight. Methods A new photogrammetry-based technique in combination with a tape-measure method was used for anthropometric measurements from nine crewmembers on the International Space Station. Measurements included circumference and height for body segments (chest, waist, bicep, thigh, calf). The time-dependent variations were also assessed across pre-, in-, and postflight conditions. Results Stature showed a biphasic change with up to 3% increase at the early flight phase, followed by a steady phase during the remaining flight. Postflight measurements returned to a similar level of the preflight. Other linear measurements, including acromion height, showed similar trends. The chest, hip, thigh, and calf circumferences show overall decrease during the flight up to 11%, then returned close to the preflight measurement at postflight. Conclusion The measurements from this study provide critical information for the spacesuit and hardware design. The ground-based assessments for spacesuit fit needs to be revalidated and adjusted for in-flight extravehicular activities from this data. Application These data can be useful for space suit design as well as habitat, vehicle, and additional microgravity activities such as exercise, where the body shape changes can affect fit, performance, and human factors of the overall design.

Experimental and numerical study on the crashworthiness evaluation of an intercity coach under frontal impact conditions

2020 ◽  
Vol 234 (13) ◽  
pp. 3026-3041 ◽  
Author(s):  
Mehmet Ali Güler ◽  
Muhammed Emin Cerit ◽  
Sinem Kocaoglan Mert ◽  
Erdem Acar
Keyword(s):  
Finite Element ◽  
Energy Absorption ◽  
Numerical Study ◽  
Absorption Capacity ◽  
The Body ◽  
Steering Wheel ◽  
Energy Absorption Capacity ◽  
Bus Structure ◽  
Bus Body ◽  
Absorption Characteristics

In this study, the energy absorption capacity of a front body of a bus during a frontal crash was investigated. The strength of the bus structure was examined by considering the ECE-R29 European regulation requirements. The nonlinear explicit finite element code LS-DYNA was used for the crash analyses. First, the baseline bus structures without any improvements were analyzed and the weak parts of the front end structure of the bus body were examined. Experimental tests are conducted to validate the finite element model. In the second stage, the bus structure was redesigned in order to strengthen the frontal body. Finally, the redesigned bus structure was compared with the baseline model to meet the requirements for ECE-R29. In addition to the redesign performed on the body, energy absorption capacity was increased by additional energy absorbers employed in the front of bus structure. This study experimentally and numerically investigated the energy absorption characteristics of a steering wheel armature in contact with a deformable mannequin during a crash. Variations in the location of impact on the armature, armature orientation, and mannequin were investigated to determine the effects of the energy absorption characteristics of the two contacting entities.

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