Conical Pendulum Research Articles

Elliptical orbits

Abstract Planets and satellites follow elliptical orbits and so does the bob of a conical pendulum. Typical orbits for a conical pendulum are calculated and compared with experimental results. Kepler’s first two laws apply to a conical pendulum but not the third law.

Dynamic balance of circles with one support point on pommel horse exercise

Double-leg circles on pommel horse exercises require a high degree of dynamic balance. However, theoretical conditions for maintaining dynamic balance are unclear. The purpose of this paper is to propose a simple theoretical model of the dynamic balance of the circles, and to illustrate its qualitative properties. To this end, the body of a gymnast is simply modeled as one rigid body with one support point, and symmetric and constant-velocity circles are assumed in most analyses. The condition that the torques of wrist and shoulder joints are zero is assumed as a dynamic balance condition with minimum strength. A control law is proposed to demonstrate the motion. Various properties of the dynamic balance condition are analyzed as follows. In the symmetric circles, (1) as the period of a circle decrease, the heights and the radius of the toes increase, and (2) the rotation of the body around its longitudinal axis in the double-leg circle has the effect of lifting the toes. (3) The shoulder and wrist torques can change the pose around the dynamic balance condition. In asymmetric circles, (4) the radius of the center of mass (CoM) increases as the angular velocity of the CoM around the support point decreases, and (5) the body angle with respect to the horizontal plane increases as the upward acceleration of the CoM increases. Moreover, mechanical principles of the circles are discussed as follows. (6) The CoM motion during the symmetric circles of the simple model can be related to the conical pendulum. In the simple model, (7) the pommel reaction force should be parallel to the arm segment when the wrist torque and the shoulder torque are equal or zero, and (8) to change the vertical component of the angular momentum of the body around the support point, the wrist torque around the vertical axis is needed. These results provide theoretical and qualitative insights into understanding and improving pommel horse exercise.

A slowly evolving conical pendulum

The idea of this work originally arose from a question pertaining to a laboratory experiment on circular motion in our departmental lab manual. The experiment itself involves rotating a bob along a horizontal circle (Figure 1), where the tension in the string attached to the bob provides the centripetal acceleration of the bob, the string itself passing through a smooth vertical pipe. It is assumed that the rotation is fast enough for the effect of gravity to be neglected and therefore the orientation of the part of the string between the top end of the pipe and the bob can be taken to be horizontal. The abovementioned question enquires what happens to the speed of the bob in the case that the bottom end of the string is hand-held and pulled slowly so that the radius of the circular orbit decreases. The answer to the question is straightforward. Either a work-energy argument or an argument involving the conservation of angular momentum provides the same correct answer.

Coriolis acceleration and critical slowing-down: A quantitative laboratory experiment

We experimentally investigate the motion of a pendulum on a turntable. The dynamics of this conical pendulum experiment are very rich and can be studied both at the undergraduate and graduate levels. At low rotational frequency of the turntable, we measure the Coriolis acceleration. Increasing the rotational frequency, we experimentally demonstrate a supercritical pitchfork bifurcation: above a critical rotational frequency, the pendulum arm spontaneously rises up. Beyond the characterization of the equilibrium pendulum angle, we evidence the so-called critical slowing down corresponding to the increase in the pendulum period when approaching the critical rotational frequency. Bifurcation and critical slowing down are key concepts in the study of critical phenomena that are seldom illustrated experimentally. All our experimental measurements are in excellent quantitative agreement with the theory we provide.

The behaviour of a forced spherical pendulum operating in a weightless environment

Summary In this article, we show that by subjecting the pivot of a simple inextensible pendulum to small amplitude high frequency rectilinear oscillations it is possible to make it operate in a weightless environment. The axis of vibration of the pivot defines a preferred direction in space and a consequential dynamical structure which is completely absent when the pivot is fixed. Using spherical polar coordinates centred at the pivot, we show that the motion of such a pendulum has fast and slow-scale components which we analyse using the method of multiple scales. The slow scale equation for the polar angle is autonomous, and a phase plane analysis reveals the essential orbital structure including the existence of conical solutions analogous to the terrestrial fixed pivot conical pendulum. In the absence of an azimuthal velocity component, its behaviour can provide a direct simulation of a plane terrestrial simple fixed pivot pendulum with a correspondingly simple form for the small amplitude period. We can also use a two-scale analysis to examine the effects of damping. Here, the slow scale polar equation has two asymptotically stable states, and we employ a combination of numerical and asymptotic analyses to elicit the slow scale orbital trajectories.

Rotational modes of a double conical pendulum

Theoretical and experimental results are presented for a double conical pendulum rotated at the top end in a circular path of radius r 0. The rotation modes are different from those with r 0 = 0 and depend on whether the two pendulum masses rotate in or out of phase with the upper end and with each other. The results extend those already described in the physics teaching literature for a single conical pendulum, would be suitable as a lecture demonstration or an undergraduate laboratory experiment, and are closely analogous to those for a chain that is rotated at its upper end.

Bioinspired, Multifunctional, Active Whisker Sensors for Tactile Sensing of Mobile Robots

Whiskers of some animals, such as rats and cats, can actively sense stimuli from their surrounding environment. Such a capability is attractive for intelligent mobile robots. However, an artificial whisker with similar abilities has not been fully developed so that the robots acquire their surrounding environment information in an active approach such as rats. In this paper, we propose a new bioinspired active whisking tactile sensor (MAWS) capable of sensing the distance, shape, size, and orientation of caves and environmental conditions. Two orthogonally distributed linear Hall sensors are mounted beneath a circular permanent magnet for spatial localization of the whisker. The whisker is then actuated and controlled by an array of nine electromagnetic coils by tuning the excitation current and phase sequence. Conical pendulum and bidirectional sweeping strategies were designed to mimic the simultaneous perception behavior of rats. A reactive obstacle avoidance experiment was also conducted to evaluate the performance of the proposed MAWS installed on a mobile robot.

Drop Tower Physics II

Drop Tower Physics (DTP) is composed of a set of experiments using standard physics lecture demonstration equipment, such as a pendulum, mass spring oscillator, and so forth, while videotaping them as they fall freely in the Dryden Drop Tower in Portland, OR. An article published in The Physics Teacher illustrated the behavior of a floating cork ball, a ball rotating inside a bowl, and a conical pendulum as their behavior changes as the acceleration due to gravity artificially transitions to zero in the non-inertial frame of reference in the drop box. This second paper is a result of dropping a mass spring oscillator, gyroscope, and chaotic pendulum. These experiments and their physical explanations are so interesting, surprising, and useful for classroom activities and discussions that they are all posted for your use on the “Drop Tower Physics” YouTube channel. Ask your students how these examples in the videos will behave when “g” transitions to zero. They will light up with excitement, ponder the possible theoretical outcomes, test those predictions with their knowledge of fundamental physics laws and principles, and then be delighted or intrigued when their prediction is correct or drastically wrong when viewing the experimental aspect of DTP videos. There are many experimental examples and explanations in the videos, but because the mass spring oscillator, the gyroscope, and the chaotic pendulum are very rich in physics theory, these explanations are given below in greater detail.

Flying Carousel Swing Physics

The conical pendulum is a classic introductory physics problem for teaching circular motion—a topic about which students frequently carry alternative conceptions. As teachers provide lessons to untangle these conceptions, it is good to allow students to practice their new knowledge in varied settings. This is one possible experiment that builds off the conical pendulum. The experiment can be modified to fit the level of complexity the instructor wishes to pursue. Although the context of this article is about the physics of the amusement park flying carousel swing, the analysis techniques discussed can be used in a variety of situations.

인체공학적 좌석이 척추와 골반 자세에 미치는 영향에 대한 생체역학적 비교연구: 원추형 진자 스툴과 반강성 유연 등받이 의자

The most common health problem caused by long-term sitting lifestyle and degenerative changes due to aging was changes in spinal pelvic posture. Sitting posture was a more complex phenomenon because it follows a change in posture. The most common working environment occurs in working with your body tilted back from a chair with a backrest. While sitting down and working, the movement of the seat plate was restricted which result in stiff lumbar spine and pelvic muscles to become stiff that eventually causes fatigue, pain and pathological posture changes. The aim of this study was to analyze the biomechanical changes and effects by evaluating and measuring the changes in spino-pelvic posture including muscle tension in sitting posture according to the type of seat used. Two different type of ergonomic seats, such as conical pendulum stool (CPS) and semirigid flexible backrest chair (SFBC), were used in a total of 17 participants. Among two types of sitting, seat-buttock contact pressure and radiographic changes of coronal trunk imbalance distance (Gravitiy line/Hip axis distance), pelvic and shoulder height differences on the seats were measured and statistically analyzed using partied t-test. The seat-buttock contact pressure reduced from 51.13 ± 32.77 Ω and 59.13 ± 39.62 Ω on initial seated to 38.57 ± 25.61 Ω and 49.37 ± 29.22 Ω on 1hr seated on CPS and SFBC, respectively (p=0.486, p=0.332). Radiographically, changes in pelvic height differed statistically significantly between two sitting types of CPS versus SFBC (average of 2.12 + 2.61 mm versus 4.29 + 4.04 mm, respectively with one hour seating, p=0.008). Improvement in shoulder height difference was statistically significant (average of 8.27 + 6.28 mm to 5.37 + 6.06 mm using CPS from initial to one hour sitting, p=0.038). CPS seating showed better biomechanical effect in reducing the imbalance between pelvic height and shoulder height through the stimulating dynamic control of spinal stability and equilibrium by activation of the upper and lower back core muscles than static ergonomic seat.

Rotational intraperitoneal pressurized aerosol chemotherapy with paclitaxel and cisplatin: pharmacokinetics, tissue concentrations, and toxicities in a pig model.

ObjectiveWe used paclitaxel and cisplatin, known to be effective in intraperitoneal chemotherapy, in a novel prototype of rotational intraperitoneal pressurized aerosol chemotherapy (RIPAC) and evaluated the pharmacokinetics, tissue concentrations, and toxicities in a pig model.MethodsWe developed RIPAC, including the nozzle with the conical pendulum motion, and used 10% of intravenous doses of paclitaxel and cisplatin. We used high-performance liquid chromatography followed by tandem mass spectrometry to analyze serum and tissue concentrations. We applied a non-compartment model to study pharmacokinetics to analyze the time-dependent serum concentrations measured before RIPAC to 48 hours. We evaluated the difference in tissue concentrations between twelve peritoneal regions by the modified peritoneal cancer index. For evaluating toxicities, we observed hepatic and renal function until 4 days after RIPAC.ResultsSix pigs underwent RIPAC using paclitaxel (n=3) and cisplatin (n=3). The peak serum concentration (Cmax) and the area under the curve were higher for cisplatin, while the time to the peak serum concentration (Tmax) was longer for paclitaxel. Moreover, the parietal peritoneum showed higher tissue concentrations than the visceral peritoneum, and the ratio of tissue to serum concentrations using Cmax was higher for paclitaxel (172.2–6,237.9) than for cisplatin (0.1–9.3). However, there were no renal and hepatic toxicities after RIPAC with paclitaxel or cisplatin.ConclusionDelayed absorption of paclitaxel sprayed by RIPAC into the peritoneum to the bloodstream may lead to higher tissue concentrations at different regions and lower serum concentrations than cisplatin.

Spatial Rigid-Flexible-Liquid Coupling Dynamics of Towed System Analyzed by a Hamiltonian Finite Element Method

An effective Hamiltonian finite element method is presented in this paper to investigate the three-dimensional dynamic responses of a towed cable-payload system with large deformation. The dynamics of a flexible towed system moving in a medium is a classical and complex rigid-flexible-liquid coupling problem. The dynamic governing equation is derived from the Hamiltonian system and built-in canonical form. A Symplectic algorithm is built to analyze the canonical equations numerically. Logarithmic strain is applied to estimate the large deformation effect and the system stiffness matrix will be updated for each calculation time step. A direct integral solution of the medium drag effect is derived in which the traditional coordinate transformation is avoided. A conical pendulum system and a 180° U-turn towed cable system are conducted and the results are compared with those retraced from the existing Hamiltonian method based on small deformation theory and the dynamic software of Livermore software technology corp. (LS-DYNA). Furthermore, a circularly towed system is analyzed and compared with experimental data. The comparisons show that the presented method is more accurate than the existing Hamiltonian method when large deformation occurred in the towed cable due to the application of logarithmic strain. Furthermore, it is more effective than LS-DYNA to treat the rigid-flexible-liquid coupling problems in the costs of CPU time.

Demonstrating Conical Pendulum Stable and Unstable States

This article analyzes and experimentally verifies the stability behavior of the equilibrium states of a conical pendulum. An analysis of the motion presents that the equilibrium states of the pendulum are determined by the pendulum angular speed. For a given pendulum length there exists a critical angular speed that determines stability conditions. Experimental results obtained using a variable speed rotator confirm the relationship between angular speed and equilibrium state conditions. An initially at rest pendulum has a stable equilibrium position that is vertically hanging straight down; however, it is shown that when gradually increasing the speed of a mechanical rotator to approach and surpass the pendulum critical speed, the initial stable equilibrium state becomes unstable. Furthermore, the pendulum, now in an unstable equilibrium, moves to a new stable equilibrium position that did not exist at speeds below the critical speed.

Large Deformation Dynamic Analysis of a Cable System by a New Hamiltonian Finite Element Method

This paper develops a new Hamiltonian nodal position finite element method for dynamic analysis of spatial flexible cable systems with large deformation. The dynamic governing equation is derived from finite elasticity theory. Logarithmic strain is applied to construct large deformation Hamiltonian canonical equations. An efficient second-order symplectic difference algorithm is built to solve the canonical equations numerically. A large strain conical pendulum system is analyzed numerically by the proposed method, and the numerical results are compared with those retracted from the existing Hamiltonian methods and Livermore Software Technology Corporation: dynamics (LS-DYNA). The proposed method is further verified by two tethered dynamic experiments involving large displacement motion and large deformation. The comparisons and verifications demonstrate that the proposed method is of symplectic conservation, has high accuracy and has stability for calculating flexible cable system dynamics with large deformation.

A conical pendulum model of a rotating chain

An experiment is described using double and triple conical pendulums to simulate the behaviour of a rotating chain. The first few rotation modes are calculated theoretically and provide good agreement with experimental results. By contrast, a chain containing many links is difficult to analyse, even though the first few nonlinear modes of a vertically suspended chain are easy to excite and are easily observed using a video camera. The experiment would be suitable as a student project since it is easy to set up and the physics is easily understood, unlike a conventional double pendulum.

Development of rotational intraperitoneal pressurized aerosol chemotherapy to enhance drug delivery into the peritoneum

This study aims to evaluate the drug distribution, tissue concentrations, penetration depth, pharmacokinetic properties, and toxicities after rotational intraperitoneal pressurized aerosol chemotherapy (RIPAC) in pigs. Because relevant medical devices have not been introduced, we developed our prototype of pressurized intraperitoneal aerosol chemotherapy (PIPAC) and RIPAC by adding a conical pendulum motion device for rotating the nozzle. RIPAC and PIPAC were conducted using 150 ml of 1% methylene blue to evaluate the drug distribution and 3.5 mg of doxorubicin in 50 ml of 0.9% NaCl to evaluate the tissue concentrations and penetration depth, pharmacokinetic properties, and toxicities. All agents were sprayed as aerosols via the nozzle, DreamPen® (Dalim Biotech, Gangwon, South Korea), with a velocity of 5 km/h at a flow rate of 30 ml/min under a pressure of 7 bars, and capnoperitoneum of 12 mmHg was maintained for 30 min. As a result, RIPAC showed a wider distribution and stronger intensity than PIPAC. Compared with PIPAC, RIPAC demonstrated high values of the tissue concentration in the central, right upper, epigastrium, left upper, left lower, right lower, and right flank regions (median, 375.5–2124.9 vs. 161.7–1240 ng/ml; p ≤ .05), and higher values of the depth of concentrated diffusion and depth of maximal diffusion (median, 232.5–392.7 vs. 116.9–240.1 μm; 291.2–551.2 vs. 250.5–362.4 μm; p ≤ .05) in all regions except for bowels. In RIPAC, the pharmacokinetic properties reflected hemodynamic changes during capnoperitoneum, and there were no related toxicities. Conclusively, RIPAC may have the potential to enhance drug delivery into the peritoneum compared to PIPAC.

Study of the Rolling Friction Coefficient between Dissimilar Materials through the Motion of a Conical Pendulum.

The rolling friction phenomenon is encountered in a wide range of applications and when two different materials are involved, quantitative characterization is necessary. The parameter to be determined is the coefficient of rolling friction, for whose estimation a methodology is proposed, based on the damped oscillation of a conical pendulum. The pure rolling contact between a sphere and a plane is obtained when a steel ball is the bob of the pendulum, which rolls on an inclined plate made from a second material from the contacting pair. The mathematical model of the motion of a conical pendulum constructed from a revolution body supported on an inclined plane in the presence of the rolling friction is developed. The dynamic equations of the rigid body with fixed point are applied and the differential equation of motion of the pendulum is obtained together with the expressions of the reaction forces in the contact point. For different pairs of materials, tests are performed on a laboratory device. The damped oscillatory motion of the conical pendulum is video-captured for the estimation of the angular amplitude variation. A program for image processing is developed for measuring the values of angular elongations from the analysis of each frame of the video and, finally, the coefficient of rolling friction is obtained. For all the materials tested, a linear decrease in angular amplitude is detected and the slope of angular amplitude can be considered as a characteristic parameter related to the coefficient of rolling friction between the two materials.

The motion of a conical pendulum in a rotating frame: The study of the paths, determination of oscillation periods, and the Bravais pendulum

In this paper, Newton's equations are solved to describe the motion of a conical pendulum in a rotating frame for the right- and left-hand conical oscillations. If the pendulum is started with the initial angular velocity (±ω0−Ωz), with ω0 being the frequency of pendulum oscillation and Ωz the angular velocity of the rotating frame around the z-axis, the paths are shown to be circular, which would apparently indicate that the Coriolis force becomes non-effective in the rotating frame. This paper explains why the paths in the rotating frame are circular, and the difference between the periods for the right- and left-handed rotations is calculated analytically. It is also shown that in an inertial frame, the conical pendulum follows an elliptical path. As the Bravais pendulum is a conical pendulum oscillating at Earth's surface, its motion is also discussed.

Structure optimization of an asymmetrically conical pendulum for energy harvesting

Structure optimization of an asymmetrically conical pendulum for energy harvesting

High-precision accelerometers-gravimeters based on fiber-optic systems

A significant advantage of fiber-optic sensors (FOS) over electrical sensors is their absolute indifference to the effects of electromagnetic interference. However, the high noise level of the low-intensity flux of high-energy photons in the measuring paths of analog FOS limits the accuracy of measuring devices based on them. The fact is that the analog modulation of any parameter in a FOS ultimately leads to fundamentally low-precision measurements of the degree of modulation of the intensity of the optical flux. The way out of this situation is the rejection of the analog and the transition to discrete modulation principles in the FOS of the optical flow parameters. To this end, in the modulation process, new parameters, additional to optical but not optical, are introduced into the optical flow, which will play the role of information carriers. This approach retains all the advantages of fiber optics (the optical stream remains the carrier of information), and transfers the problem of measurement accuracy to other, non-optical areas where it is properly solved. The possibility of constructing precision accelerometers (gravimeters) with measuring transducers based on new-class FOS with pulse modulation of the optical flux intensity (IFOS) is considered. The sensitive element of such an IFOS is a conical pendulum, on the basis of a cantilever mounted piece of quartz optical fiber, on the free end of which there is an inertial mass. High values of the metrological parameters of the accelerometer based on the IFOS are ensured by the possibility of precise measurements of the temporal parameters of the sequence of optical pulses generated by it. The processing of signals from the IFOS is carried out by methods and means of digital technics, which eliminates the possibility of introducing a signal processing error and allows purposefully correct the measurement results. Thanks to this, it is possible to neutralize the influence on the measurement results of both the natural flaws and imperfections of the IVOD, as well as the errors of their manufacture and adjustment. The study of the mathematical model of IFOS with real values of its design parameters and the frequency of the generator of counting pulses confirmed the possibility of obtaining high values of its metrological characteristics: the threshold sensitivity is up to 10-13 g, and the dynamic range of the measured accelerations is up to 109. These figures should be considered as illustrative. The principle of construction of the IFOS design makes it possible to easily change its metrological parameters over a wide range by a corresponding change in both the parameters of the elements of its construction and the frequency of the counting pulse generator.