Momentum Change Research Articles

Momentum in Tennis Echoes in each Bounce

The 2023 Wimbledon Gentlemen’s final unfolded as a remarkable battle, characterized by momentum shifts. However, it is challenging to measure momentum and its effect on the events during the match. This article primarily focuses on how to quantify and evaluate momentum, predict the swings of the match, test the generality and provide useful advice to players and coaches. Firstly, we conduct data pre-processing by removing outliers on the given data according to the tennis rules. Next, in order to identify which player is performing better, we select 10 secondary indicators based on Spearman Correlation Coefficients, such as distance and rally_count from two aspects: technique and physiology. Then, we combine CRITIC method to calculate the weights of related indicators and TOPSIS method to evaluate the performance. The result indicates that the model can capture the flow of the match and Carlos Alcaraz performs better by a higher momentum of 0.06 in the given data with match_id of 2023-wimbledon-1301. Then, to assess the coach’s claim regarding the role of momentum in the match, we establish a model for on-court situation changes using statistical methods and compare it with CRITICTOPSIS model. By comparison, we conclude that the change in momentum trend shows a 59% correlation with the outcome of the next point and there is a clear correlation between the changes in Momentum and on-court situation. That is to say, momentum do play a role in the match.

A momentum quantification method for tennis matches based on t-SNE and k means clustering

Momentum is a crucial factor influencing the outcomes of sports competitions. This study proposes a method for visualising and quantifying momentum using various modern analytical techniques. These techniques include feature engineering, dimensionality reduction with the t-SNE algorithm, and k-means clustering. By analysing data from the past five years of Wimbledon, the study extracted various performance features such as serve success rate and scoring rate. By calculating the similarities between features and conducting cluster analysis, the study reveals changes in momentum during matches. This research employs data visualisation and clustering results to not only display the conditions of matches under different momentum states but also quantifies momentum changes by calculating the Euclidean distance between data points and cluster centroids and standardising these distances using the Z-score method. This approach provides a visual perspective that reveals the dynamic changes that occur within matches and quantifies momentum. It demonstrates that these changes in momentum can indeed reflect the progression and outcomes of matches.

Hawking Temperature Modification and the Physical Dynamics of Black Holes: A Study of the Influence of Internal and Cosmological Variables

<p>The main objective of the study is to develop a model that modifies the traditional Hawking temperature by considering the influence of internal variables such as radius, mass, electric charge, angular momentum, and cosmological constant. The research method involves mathematical analysis and computational modeling based on the modified Hawking temperature equation. The results show that the modified Hawking temperature produces non-linear corrections that show the interaction between black holes and the quantum structure of spacetime. graphical representations visualize the variation of Hawking temperature with changes in area, electric charge, angular momentum, and cosmological parameters. The implications of the research extend to the understanding of the thermal properties of black holes in the context of gravitational and quantum theories. The research identifies gaps in the knowledge of the effects of cosmological parameters on black hole thermodynamics and introduces Hawking temperature modifications that have not been mapped in detail before. The study concludes that the Hawking temperature modification provides a strong foundation for further research in black hole physics, particularly in the effect of physical and cosmological parameters on the thermal properties of black holes.</p>

Vortex lattice state transitions in water surface waves

Surface waves can generate an ordered vortex lattice of fluid particles on the air-water interface. Here, the transitions of the lattice structure are observed through experiments and modelled analytically. A fully-immersed square waveguide system is positioned at the center of a larger bath which directs particles into counter-rotating vortices. Flow interactions with the bath free-surface alter the ordered structure, and a state transition is initiated by the increase of the waveguide immersion depth. It manifests as a change in the orbital momentum and spin properties of the vortices, and develops through the combination of reflected-wave attenuation and mean flow effects from the classical Stokes drift and Eulerian currents. Transitions from a perfect antiferromagnetic state to weakly-ordered ones are achieved, including a monopole vortex reminiscent of spectral condensates in thin fluid layers. Order in the disordered flow is uncovered through velocity field corrections after invoking time-scale separation. The lattice structures are modelled analytically through a superposition of mean flow contributions from the waveguide and bath modes. The results open a new platform for investigating the dynamics of wave and vortex lattice interactions, and devising new techniques to characterize complex flow phenomena on the air-water interface.

Pickleball sounds: impact induced vibration and radiated sound

The rapid growth in popularity of pickleball and the ever-increasing number of pickleball courts has resulted in growing concerns about the effect of pickleball sounds on nearby neighbors. The vibration of the ball and paddle that is generated at impact, and which is the source of the radiated sound, was measured for different paddles as a function of frequency using an impact hammer instrumented with a force gage. Average vibration velocities over the paddle surface were generated that scale the radiated sound. Animations of paddle vibration were also generated. A paddles vibration level depends on its internal mechanical damping which was also measured. A performance metric is proposed where the paddles' sound levels are compared at the same "power" in terms of the change in momentum (velocity) of the pickleball on impact. Outdoor directivity measurements of the sound for a paddle were "dipole-like" in character with lower levels, by 10 dB or more, in the plane of the paddle compared to levels perpendicular to its face. The orientation of the courts may be important if the sound levels during play are quieter in the general direction along the nets.

Periodic Rolling and Bumping

Abstract We consider a sphere that rolls down an inclined corrugation of identical, frictional circular cylinders in contact. We assume that the motion is a periodic succession of rolling and bumping that results in a velocity that is, on average, steady. We use balances of force and moment and impulse and momentum change to calculate the instantaneous and average velocities, the tangential and normal contact forces, and their ratio in rolling regimes that involve no sliding, some sliding and a transition between these at contact. We compare the predictions for the steady average velocity versus the inclination for different sphere to cylinders radii ratio and the predictions for the angle of inclination versus the radii ratio for stopping, initiation of sliding and loss of contact with the results of numerical simulations.

The First Law of Newton. Formula and Consequences: Changes in Weight and Forward Motion of Rotating Bodies

The aim of this work is to show that the first Newton’s law (law of inertia) is a manifestation of the law of conservation of angular momentum in the physical vacuum. The force of inertia arises in a body as a result of a change in the angular momentum of the body. The change in the angular momentum can emerge when changing the characteristics of spins of virtual photons created by quantum objects constituting the body. Due to the law of conservation of angular momentum a change in the angular momentum results in emergence of the processes compensating this change. One of these compensating processes is the emergence of force of inertia influencing the velocity of quantum objects constituting the body. Another compensating process is the emergence of rotation of these objects. Both these processes are observed in experiments. The force of inertia may arise in rotating bodies as rotation of body influences the characteristics of spins of virtual photons created by quantum objects of rotating body. If the force is directed along the vector of gravitation, the weight of rotating body is increased. If the force is directed against the vector of gravitation, the weight of rotating body is decreased. If the force is directed perpendicular to the vector of gravitation, the body is moving along the Earth surface. All these phenomena are observed in experiments.

A Study of Momentum Change in Sports Competitions Based on Evaluation and Correlation Analysis

A Study of Momentum Change in Sports Competitions Based on Evaluation and Correlation Analysis

Technical fouls as a trigger of momentum change: analysis of two decades of NBA data

ABSTRACT In an analysis of NBA big data (4,196 cases over 21 seasons; 2000–2021), we examined the effect of technical fouls (TFs) on game momentum. Considering leading or trailing positions in home and away games, we studied performance metrics like points, rebounds, assists, and fouls across immediate, short-term, and medium-term timeframes. Using a quantitative methodology, the results showed that TFs were primarily called on the home team's coach (66.1%) when his team was trailing and the away team's coach (78.1%) when his team was at a disadvantage. Overall, TFs were called in 72.5% of the cases when the team was in a losing position. Furthermore, when the home team's coach was penalised with a TF, the home team secured victory in 44.2% of instances, while the away team won only in 28.1% of games played on the away team's court. Rebounds and fouls were the most pronounced performance indices to change after a TF call. The psychological state, which precedes and proceeds the TF calls, is considered the main reason for the momentum change. By and large, during crises, coaches can prioritise TFs calls, especially in home games, to boost psychological momentum. TFs can initiate team decline and boost scoring by decreasing personal fouls and increasing defensive rebounds. Future research is required to explore TFs’ effects within game quarters and differences between regular season and playoff games for further insights.

A Comparative Analysis of the 2021 NFL Combine Data: The Relationship Between Linear Sprint, Momentum, Vertical and Horizontal Jumps and Change of Direction Deficit

The majority of COD execution assessments employ the use of total time as the metric by which COD performance is judged. This study investigated the relationships between CODD time, sprint time, 5-10-5 and jump performance. Performance data of 328 participants of the 2021 NFL Combine (age: 22.35 ± 1.00 years; height: 1.87 ± 0.07m; weight: 108.51 ± 21.61kg) was collected and used for the analysis. CODD correlated to the 5- 10-5 pro-agility (r= 0.69 - 0.71) test but not sprint time (r= 0.15 - 0.27) for both the drafted and undrafted groups. Meanwhile, there was a large to very large association between 5-10-5 proagility time and the sprint variables (r = 0.62 - 0.82) for both drafted and undrafted groups. The correlation between CODD time and momentum was minor (r= 0.26 – 0.28) for both drafted and undrafted groups, but the 5-10-5 pro-agility reported a strong to a very strong association with momentum (r= 0.57 – 0.75). There was an inversely small correlation between CODD time and VJh (r= – 0.27) and BJ (r= -0.25– -0.28) for both drafted and undrafted groups whereas the 5-10-5 pro-agility time reported an inversely large to very large correlation with VJH (r= -0.51 – -0.68) and BJ (r= -0.57 – -0.71) on both groups. The magnitude and impact of the momentum, horizontal jump, and vertical jump of participants on their CODD time indicate that coaches and fitness experts should focus on improving the technical aspects of the COD execution when attempting to improve their CODS.

Boundary layer flow and heat transfer enhancement by utilizing Casson ternary nanofluid past a horizontal cylinder in a non-Darcy porous medium with thermal radiation effects – Non-similar solutions

The aim of this study is to examine the results of MHD, radiation and Casson ternary fluid over a horizontal cylinder with a saturated porous medium. The nanofluids used in this study are trihybrid, consisting of Cu, Al2O3 and Tio2 particles suspended in blood as the base fluid. The dimensional form of governing equations is transformed into dimensionless form by manipulating non-similar solutions. The conservation equations are solved using the Keller Box Method (KBM). The presence of several emerging dimensionless parameters, namely the Casson fluid parameter (β), Darcy number (Da), Forchheimer parameter (∧), radiation parameter (Rd) and magnetic field (M) on fluid momentum and energy changes in the boundary layer regime are investigated in detail. The Prandtl value (Pr) for blood is determined to be 21. The application of porous medium models spans across various fields, including engineering, environmental science, biology, and materials science.

Investigation on spray combustion modeling for performance analysis of future low- and zero-carbon DI engine

Global warming issues and fossil fuel depletion crisis have forced transportation industry to seek clean engine fuels both liquid and gaseous. Dual-fuel mode with high-pressure direct injection (HPDI) has been recognized as mainstream method in developing flexible-fuel internal combustion engines (ICEs). But flexible-fuels’ physicochemical properties and spray combustion characteristics under HPDI have changed a lot. Unfortunately, there is currently no universal model for predicting spray combustion behaviors and analyzing performance of flexible-fuel ICEs. Therefore, this paper aims to develop a novel spray combustion model and provide optimal injection and combustion strategies for performance improvement of low- and zero-carbon HPDI ICEs. Based on balance of momentum change and vortex ring drag force, the jet spray effective injection velocity is obtained. Then the jet spray penetration under varying injection rate is solved. Finally, the developed model is established and validated experimentally, with the spray combustion characteristics of various fuels investigated. The results show that the developed model has a good accuracy and robustness for flexible-fuels’ characteristic analysis. Meanwhile, multiple-injection could increase the combustion efficiency (CE) over 10.27 % than single-injection, and CE increases with dwell time. Moreover, CE of H2 in nitrogen-oxygen (N2–O2) atmosphere is 10.15 % higher than that in argon-oxygen (Ar–O2) atmosphere.

Unveiling the Deep Connection Between Athlete Momentum and Match Scoring through Statistics Analysis

The concept of momentum in ball sports is characterized by significant changes in-game performance and mental states, which play a key role in determining the outcome of a match. This study takes the 2023 Wimbledon men's final as an example and constructs a model for assessing athletes' performance during tennis matches based on binary logistic regression. It also constructs a tennis match momentum assessment algorithm to explore the relationship between the momentum change among match players and the performance change (score difference) of both players. It was found that the momentum change of match players was closely related to the score difference. This study is not only conducive to improving the athletes' competitive level but also has a profound impact on the scientific and professional development of tennis.

A study of tennis match trend prediction based on momentum assessment and heuristic HMMs

In competitive tournaments, there exists a currently unexplored factor, momentum, whose role affects the trend of the game to a certain extent and even produces surprising fluctuations, which is particularly evident in tennis.This paper proposes a feasible research programme for the problem of momentum change and trend prediction in tennis matches. Firstly, hundreds of matches of Wimbledon Tennis Championships were used as the data source, and the assessment indexes related to momentum were filtered and mathematical models were established through analysis and processing, and then the coefficient settings were optimised by using the self-looping simulated annealing algorithm. The final model better describes changes in match conditions, with a model fit of over 85% for 87% of the matches.At the same time, in order to verify the existence of correlation between the momentum and the direction of the game, this paper randomly selects a number of games, the first half of the event as a dataset for the momentum model training, and uses the heuristic HMM to predict the subsequent changes and compare them with the scoring difference in the second half of the actual game, and the test result is that the two have basically the same trend, and therefore it can be proved that the momentum change curve can be used as one of the indicators of the prediction of the game trend.

Quantification of momentum in tennis matches and its impact: a study based on AHP-EWM method and data analysis

Tennis is a globally popular sport that tests players' abilities in all aspects, including mental quality. In tennis, momentum is a psychological phenomenon that reflects the strengths and weaknesses of players. It affects players' mentality, performance, and match results. However, there are still some inadequacies and controversies in the current research on momentum, such as its concept, formation mechanism, quantification method, and actual effect. This study deeply analyzes the concept and formation mechanism of momentum in tennis matches and its influence on the result of the match. Through a combination of data analysis and quantitative methods, this study reveals the importance of momentum changes on player performance and match results. Through the application of AHP-EWM, Welch's T-Test, and Run Test, this paper not only quantifies momentum but also confirms the significance and non-randomness of momentum, refuting the traditional views on the randomness of competition performance fluctuation and success rate. The results of this study not only provide a new perspective for understanding the strategy and dynamics of tennis matches, but also provide practical guidance for athletes' training and competition preparation. In addition, the methodology and findings of this study also have reference value for other sports that need to analyze the impact of momentum, opening up a new path for future sports science research.

An assessment measurement study based on the momentum of the tennis ball in question

In tennis, it is very important to always be aware of the movement and trend of the match. Accurately grasping the change of momentum is of great practical significance in predicting the future fluctuation of the match. Based on the relevant match data provided by Wimbledon, three models are constructed in this paper. Model one is a win-loss probability model based on binomial distribution, which deflates the impact of each small game win on the whole game, and accurately calculates the overall win rate of current players by judging the difference in players' level as well as the number of games won and lost. Model 2 is a momentum calculation model, which accurately describes the player's game status by analyzing the number of consecutive scores, score gap, number of key balls, and number of errors in a multi-dimensional analysis, and then accumulating and calculating the momentum data. Model 3 is a match fluctuation prediction model constructed based on Gradient Boosting Tree, which is utilized to predict match fluctuations by comparing predicted fluctuations with actual fluctuations on the test set in the tournament. And it evaluates which factor is the most important in predicting the future trend.

Power Extraction Performance by a Hybrid Non-Sinusoidal Pitching Motion of an Oscillating Energy Harvester

This study proposes a hybrid pitching motion for oscillating flat plates aimed at augmenting the energy extraction efficiency of an energy harvester. The proposed hybrid pitching motion, within the first half cycle, integrates a non-sinusoidal movement starting at t/T = 0 and progressing to t/T = 0.25, with a sinusoidal movement initiating after t/T > 0.25 and continuing to t/T = 0.5. The second half of the cycle is symmetric to the first half but in the opposite direction. The calculated results show that the proposed hybrid pitching motion outperforms both the sinusoidal and the non-sinusoidal motions. The hybrid pitching motion merges the merits of both the sinusoidal and non-sinusoidal motions to optimize pitch angle variation. This integration is pivotal for enhancing the overall power output performance of an oscillating energy harvester characterized by momentum change that enhances the orientation of the heaving movement, smoother motion transitions, and consistent energy harvesting. The power generation is obtained at wing pitch angles of 55°, 65°, 70°, 75°, and 80° during a hybrid pitching motion. The proposed hybrid pitching motion, set at a pitch angle of 70°, achieves a maximum power output that exceeds the oscillating flat plate using a sinusoidal pitching motion by 16.0% at the same angle.

Revealing the Close Connection Between Tennis Match Momentum and Victory Through Machine Learning Methods

In competitive sports, especially in tennis matches, momentum is considered a key factor influencing the outcome. However, there is widespread controversy surrounding the definition of momentum, its quantification methods, and its impact on match results. We compared different models (LightGBM, SVM, XGBoost, MLP, logistic regression) using five-fold cross-validation to predict changes in momentum in tennis matches based on a given dataset. The results showed that LightGBM performed best with an accuracy of 77.6%. We selected LightGBM to predict the momentum score for each point of player 1 in the final match. It was found that the average momentum scores in the second, third, and fifth sets were greater than 0.5, which aligned with the actual outcomes. Furthermore, through Pearson correlation analysis and OLS validation of the relationship between momentum changes and match results, we obtained a p-value below 0.05, a Pearson correlation coefficient of 0.59, and an F-statistic of 376.6 in the OLS model, indicating a strong positive correlation between the two.

Research on Momentum Analysis of Tennis Match Based on Machine Learning

This study aims to quantify momentum changes in tennis matches by building a machine learning model and investigate their impact on match outcomes. Firstly, a momentum model is established to quantify the momentum value of players by defining basic points, break points, guaranteed points and continuous points. Then, the momentum curve of players is calculated using real match data, and its high match with the match trend is verified. Then, the correlation between momentum value and match result is tested by statistical test method. The results show that there is a significant correlation between momentum value and match victory. Further, the displacement test verifies that the change of momentum value is not random, but reflects the actual trend of the game. This study proves that momentum plays an important role in tennis matches, and its change has a significant impact on match results, which provides an important reference for further research and application of momentum.

Insights into the Tennis Court through Machine Learning: Analysis and Evaluation of the Wimbledon Men's Singles Final

In today's data-driven world of sports science, in-depth analysis of tennis match data is especially critical for improving athlete performance, refining training strategies, and enhancing the viewing experience. This study starts from all aspects of data and key features of the players during the game, using Stacking integrated machine learning methods, a kind of integrated algorithms through XGBoost, GBDT, CatBoost, and ExtraTrees to build prediction models, aiming to always keep an eye on the dynamics of the game, using the data to reveal the changes in the player's strength and to quantify the impact of the momentum on the player as well as the game's trend. The experimental results show that we have identified factors that influence changes in players' momentum, which can provide real-time feedback to coaches and players so that they can make data-based decisions during matches, opening up new avenues for improving tennis players' scoring ability and maximizing help for players to improve their winning percentage in matches.