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Full-Text Articles in Engineering

String-Of-Pearls Measurements Of Supersonic Plasma Jets Using Magnetospheric Multiscale Satellites, Amelia Koth Aug 2026

String-Of-Pearls Measurements Of Supersonic Plasma Jets Using Magnetospheric Multiscale Satellites, Amelia Koth

Discovery Day - Daytona Beach

High-energy supersonic plasma jets form when the solar wind, which is a flow of charged particles from the Sun, slows down as it encounters Earth’s magnetic shield. Occasionally, the solar wind remains at supersonic speeds as it enters this region. This forms plasma jets that propagate toward Earth; these jets can carry strong magnetic fields, drive magnetic reconnection, and potentially initiate substorms that lead to auroral activity.   Previously studied plasma jets occurred when the interplanetary magnetic field (IMF) points southward. In contrast, this study focuses on northward IMF conditions, which are less understood, yet still capable of producing supersonic jets. …

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Helio: Heliophysics Enhanced Learning For Intelligent Orbits, Kylie Nager, James Kirk Aug 2026

Helio: Heliophysics Enhanced Learning For Intelligent Orbits, Kylie Nager, James Kirk

Discovery Day - Daytona Beach

HELIO: Heliophysics Enhanced Learning for Intelligent Orbits   Satellite constellations operating in near-Earth space are increasingly vulnerable to space weather disturbances, such as solar flares, coronal mass ejections (CMEs), and high-speed solar wind streams, which degrade communications, destabilize attitude control, and accelerate orbital decay. These disturbances directly threaten mission continuity, constellation availability, and space asset survivability. Current protective approaches rely primarily on ground-based alerts and lack integration with broader space domain awareness, which results in programmed reactive protocols that are often initiated too late to prevent performance degradation and asset loss. The HELIO project addresses this gap by turning space-weather forecasts …

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Interplanetary Trajectory Optimization With Reinforcement Learning, Shiloh Cuffe Aug 2026

Interplanetary Trajectory Optimization With Reinforcement Learning, Shiloh Cuffe

Discovery Day - Daytona Beach

This project investigates the application of reinforcement learning (RL) to optimize low-thrust interplanetary trajectory design, focusing on the Earth-Venus transfer leg of the BepiColombo mission. Traditional trajectory optimization methods, such as patched conics and genetic algorithms, often require simplifying assumptions or complex optimization schemes. This work formulates the trajectory design problem as an optimal control problem (OCP) within a Markov Decision Process (MDP) framework, enabling an RL agent to learn efficient transfer strategies under realistic spacecraft constraints. The objective is to develop an autonomous guidance approach capable of replicating or improving upon established mission designs. The spacecraft is modeled as …

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Generalized Cloud-Based Compressible Aerodynamics Calculator And Simulation Web App, Massimo Mansueto, Liam Griesacker, Andres Torres-Figueroa Aug 2026

Generalized Cloud-Based Compressible Aerodynamics Calculator And Simulation Web App, Massimo Mansueto, Liam Griesacker, Andres Torres-Figueroa

Discovery Day - Daytona Beach

The Generalized Cloud-Based Compressible Aerodynamics Calculator and Simulation Web App focuses on the development of a tool to support the analysis, visualization, and teaching of compressible aerodynamics. In the case of most undergraduate aerospace engineering courses, students rely on static equations, charts, and manual calculations, which can make it difficult to conceptualize complex flow phenomena such as shock waves, expansion fans, and nozzle flow. The purpose of this project is to create an accessible platform that integrates a compressible flow calculator, nozzle sizing tool, and interactive simulations into a single educational resource. The application is implemented using modern web development …

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Extending The Essentially Entropic Lattice Boltzmann Method To Three-Dimensional Turbulent Flows, Michael Derderian Aug 2026

Extending The Essentially Entropic Lattice Boltzmann Method To Three-Dimensional Turbulent Flows, Michael Derderian

Discovery Day - Daytona Beach

The Entropic Lattice Boltzmann Method (EELBM) has demonstrated strong numerical stability and accuracy for two-dimensional simulations, particularly at higher resolutions where the entropic formulation introduces only minimal stabilizing turbulent viscosity and eventually converges to the Lattice Bhatnagar–Gross–Krook (LBGK) formulation. This built-in stabilization can be interpreted as an implicit large-eddy simulation (LES) model, allowing EELBM to capture complex turbulent behavior without requiring explicit subgrid-scale closures. While these advantages have been thoroughly validated in 2D, understanding how the entropic constraint regulates dissipation in three dimensions is essential for assessing EELBM’s suitability for practical, turbulence-dominated applications. This work focuses on the development and …

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Feasibility Of High-Throughput Onboard Ai For Mars Rovers Under Solar Constraints, Aashman Gupta Aug 2026

Feasibility Of High-Throughput Onboard Ai For Mars Rovers Under Solar Constraints, Aashman Gupta

Discovery Day - Daytona Beach

This project evaluates the feasibility of sustained onboard AI autonomy for a solar-powered Mars rover by directly linking solar energy availability to achievable compute performance. While Mars solar irradiance and edge computing performance have been studied independently, no unified framework currently couples surface power generation to autonomy throughput in an experimentally validated manner. The project will begin with a simulation of solar power generation for a 1 m² rover-mounted array across a Martian sol, accounting for seasonal variation, dust opacity, and array configuration (fixed versus sun-tracking). The resulting power profile will then be coupled to representative compute platforms running autonomy …

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An Energy-Aware Meta-Learning Framework For Real-Time Lunar Rover Localization Via Adaptive Algorithm Selection, Jose Demedeiros, Garrett Seyler Aug 2026

An Energy-Aware Meta-Learning Framework For Real-Time Lunar Rover Localization Via Adaptive Algorithm Selection, Jose Demedeiros, Garrett Seyler

Discovery Day - Daytona Beach

This work proposes an energy-aware meta-learning framework that selects the single most suitable localization algorithm for a lunar rover, per scene, using only monocular imagery and orbital maps. The goal is to achieve sub-meter accuracy while minimizing onboard compute and energy consumption. We assemble a suite of seven lunar-relevant algorithms spanning relative and absolute localization, including monocular ORB-SLAM3, LuVo homography-based visual odometry, Censible cross-view matching with orbital imagery, crater-based methods (LunarNav and ShadowNav), monocular horizon navigation with a DEM, and DROID-SLAM. Relative methods provide incremental motion updates, while absolute methods deliver global pose fixes; an Extended Kalman Filter fuses these …

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A System Safety Approach To Assuring Artificial Intelligence Enabled Functions In Civil Aviation, Evan Bear, Quinn Galen Aug 2026

A System Safety Approach To Assuring Artificial Intelligence Enabled Functions In Civil Aviation, Evan Bear, Quinn Galen

Discovery Day - Daytona Beach

Artificial intelligence and machine learning techniques are increasingly proposed for use in safety-critical civil aviation functions including perception decision support and pilot assistance. Existing aviation safety and certification standards such as ARP4754A and DO-178C were developed under assumptions of determinism explicit requirements and complete behavioral specification which do not directly apply to learning-enabled systems. This mismatch has created uncertainty regarding how artificial intelligence enabled avionics can be safely assured and certified. This paper presents a system safety approach for assuring artificial intelligence enabled functions within existing aviation certification frameworks. In this approach safety assurance is based on explicitly identifying the …

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A Hybrid Llm-Srgm Framework For Ai-Enabled Reliability Assessment In Safety-Critical Software Systems, Caleb Stone, Shrenik Jadhav Aug 2026

A Hybrid Llm-Srgm Framework For Ai-Enabled Reliability Assessment In Safety-Critical Software Systems, Caleb Stone, Shrenik Jadhav

Discovery Day - Daytona Beach

Ensuring the reliability of software intensive and safety critical systems is a persistent challenge across aerospace, defense, transportation, and other mis- sion focused domains. Traditional software relia- bility growth models (SRGM) provide useful quanti- tative insight into defect discovery trends, but they rely mostly only on numerical failure data and do not use the rich contextual information contained in test logs, anomaly reports, and engineering notes. This paper presents a hybrid framework that com- bines semantic features extracted by a large lan- guage model (LLM) with a non-homogeneous Pois- son process (NHPP) based software reliability growth model. The LLM analyzes …

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Cars Imass - Comparing Llm Vs Human Operator Effectiveness In Multi-Agent Swarm Coordination, Gatlin Nelson Aug 2026

Cars Imass - Comparing Llm Vs Human Operator Effectiveness In Multi-Agent Swarm Coordination, Gatlin Nelson

Discovery Day - Daytona Beach

Title: Dual-Perspective Risk Analysis for Human-LLM Decision Comparison in UAV Swarm Navigation   Unmanned aerial vehicle (UAV) swarms operating in low-altitude wireless network environments encounter localized disruptions that degrade positioning and navigation metrics. These disruptions are modeled as geographic failure zones with defined boundaries. A UAV discovers a zone by entering it and observing degraded performance on its onboard systems. This work assumes that affected UAVs can autonomously retreat to safety using onboard sensors and focuses on the subsequent rerouting decision. Once recovered, the system generates candidate repositioning points surrounding the vehicle, each scored using Conditional Value-at-Risk (CVaR). A human operator …

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Multi-Dimensional Particle-In-Cell With Monte Carlo Collisions (Pic-Mcc) Simulation For Visualizing Plasma Flow And Secondary Ionization In Constricted-Anode Geometries, Parth Thakar Aug 2026

Multi-Dimensional Particle-In-Cell With Monte Carlo Collisions (Pic-Mcc) Simulation For Visualizing Plasma Flow And Secondary Ionization In Constricted-Anode Geometries, Parth Thakar

Discovery Day - Daytona Beach

Constricted-anode plasma sources generate locally intensified electric fields that enhance ionization near the anode, making them valuable in propulsion and laboratory plasma systems. However, the narrow geometry produces complex charge accumulation and secondary ionization effects that remain difficult to measure experimentally. To address this challenge, our research develops and applies a multi-dimensional Particle-in-Cell with Monte Carlo Collisions (PIC-MCC) simulation of a DC discharge in 1-D, 2-D, and 3-D configurations that model a constricted-anode device. PIC-MCC is a first-principles method that tracks electrons and ions individually while computing self-consistent electric fields and incorporating energy-dependent collision processes. This approach enables direct visualization …

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Phaëthon System, Brady Roudabush, Lauren Gallo, Emelia Thompson, Jacob Woods Aug 2026

Phaëthon System, Brady Roudabush, Lauren Gallo, Emelia Thompson, Jacob Woods

Discovery Day - Daytona Beach

Phaëthon System is the project name for the Search and Rescue Drone Initiative. This initiative will improve the current search and rescue drone industry by introducing new techniques to get through dense forest canopies and other places where an overhead view is not useful. The Phaëthon System uses a swarm of drones that can penetrate under the tree canopy to map and search with the utmost efficiency and safety for rescuers. A command drone is launched to survey the overall search area, and set up a communications and data link. The next component is then released, which is a swarm …

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Real-Time Fused Sensor System For Early Onboard Detection Of Weather Phenomena, Sanjana Singh Aug 2026

Real-Time Fused Sensor System For Early Onboard Detection Of Weather Phenomena, Sanjana Singh

Discovery Day - Daytona Beach

Weather-related hazards continue to be a major cause of operational interruptions and safety issues in the aviation sector. Atmospheric phenomena, including turbulence, microbursts, convective storms, and rapidly changing boundary-layer conditions, can arise quickly and often occur on spatial scales that are not adequately addressed by regional forecasting systems. These phenomena particularly endanger aircraft flying at low altitudes, such as general aviation planes, unmanned aerial vehicles (UAVs), and those during takeoff and landing Although meteorological forecasting systems and ground-based radar networks offer important regional insights, they may fail to detect localized atmospheric variations encountered along specific flight routes. Consequently, pilots and …

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Reimagining Wind Based Sea Travel With Vertical Axis Wind Turbines, Julian Goins Aug 2026

Reimagining Wind Based Sea Travel With Vertical Axis Wind Turbines, Julian Goins

Discovery Day - Daytona Beach

In the realm of Nautical vehicles, aside from the occasional outliers like rarely used coal steamboats, experimental solar powered ships, or the military grade nuclear vessels, the vast majority of ships run off diesel-powered engines. The unsustainability of such methods will need to be addressed for the security of our planet’s future due to the limited and destructive nature of fossil fuels, much like it already is in many other fields. To that end, this project gains inspiration from the past and looks toward harnessing the power of the wind. In recent times, most sail boats are equipped with some …

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Investigating The Spatial Scales Of Ionospheric Irregularities Using Wavelet Analysis, Nash Mcleod Aug 2026

Investigating The Spatial Scales Of Ionospheric Irregularities Using Wavelet Analysis, Nash Mcleod

Discovery Day - Daytona Beach

Investigating the Spatial Scales of Ionospheric Irregularities Using Wavelet Analysis:   Ionospheric radio wave scintillation arises from plasma density irregularities in Earth’s ionosphere. Consequently, rapid fluctuations occur in the phase and amplitude of Global Navigation Satellite System (GNSS) signals and can impact communication and navigation systems. These irregularities span from a wide range of spatial and temporal scales and evolve dynamically under the influence of magnetosphere-ionosphere (MI) processes. We investigate phase and amplitude scintillation events using Continuous Wavelet Transform (CWT) to study the spatial evolution of ionospheric irregularities. These irregularities are thought to be formed via different plasma mechanisms such as …

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Effect Of Anode Size On The Properties Of Constricted Hollow Anode Pulsed Plasma Source, Nirav Patel, Garret Seckinger Aug 2026

Effect Of Anode Size On The Properties Of Constricted Hollow Anode Pulsed Plasma Source, Nirav Patel, Garret Seckinger

Discovery Day - Daytona Beach

With the advent of ion thrusters, burns requiring large velocity changes can be performed with a fraction of the propellant required by traditional chemical rocket engines. However, current ion thrusters produce thrust in the order of millinewtons and thus cannot be viable for launching vehicles or burns requiring velocity changes in a small amount of time. Furthermore, current ion thrusters experience grid and component erosion, where the two grids at the termination of the nozzle slowly erode due to particle impact, and the hot electrodes degrade due to high thermal load. This limits the life of ion engines, which require …

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Accelerating Search And Rescue Response: A Simulation Study On The Dynamic Efficiency Of Flocking-Enabled Drone Swarms, Sophia Beckwith, Carys Del Prete Aug 2026

Accelerating Search And Rescue Response: A Simulation Study On The Dynamic Efficiency Of Flocking-Enabled Drone Swarms, Sophia Beckwith, Carys Del Prete

Discovery Day - Daytona Beach

This project explores how imitations observed in animal group behavior, specifically flocking in birds, can be applied to the functionality of autonomous drone systems to aid in search and rescue efforts. The goal is to demonstrate how incorporating code based on the Boids, Vicsck and predictive control linear algebraic mathematical models for drone flight controls and the collective behaviors of flocks will increase the efficiency of drone maneuvers, allowing them to reorganize and fill gaps when one is removed. A MATLAB-based simulation was developed to model the behaviors using research conducted on the symmetric and synchronized behaviors observed from flocks …

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A Feedback Loop Control To Automate Cold Atmospheric Pressure Plasma Based Additive Manufacturing, Arineh Shahbazi Aug 2026

A Feedback Loop Control To Automate Cold Atmospheric Pressure Plasma Based Additive Manufacturing, Arineh Shahbazi

Discovery Day - Daytona Beach

Currently, nanoparticle annealing based additive manufacturing process requires high temperatures, making them unsuitable for a broad range of applications. By lowering the temperature and developing a process to use Cold Atmospheric Pressure Plasma (CAPP) for annealing, many more doors are opened to a wide range of materials, films, and environments for space, communication, and microelectronics. CAPP-based additive manufacturing technology is continually evolving, making projects like nanoparticle annealing more feasible. In this work, we designed a CAPP jet printer assembly consisting of a 0.25-inch outer diameter glass tube connected to a 3D printing nozzle. The flow of Argon gas in the …

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Climate Resilient Infrastructure: The Problem Shift, Tyler Lautieri, Isaiah Morrison, Harrison Totten Aug 2026

Climate Resilient Infrastructure: The Problem Shift, Tyler Lautieri, Isaiah Morrison, Harrison Totten

Discovery Day - Daytona Beach

Climate change is a heavily debated topic, but recent studies and data show that climate change is leading to an increase in the frequency and severity of hazards. Infrastructure systems are subjected to more compound and cascading events that lead to the degradation of the systems. More traditional infrastructure design relies on concern that the system will be subjected to single hazard issues, and the design focuses on preventing structural failure during these isolated events. These approaches often fail to account for long term degradation of the system, as well as the interacting hazards, and system interdependence, which makes resilience …

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Optimization Of Engine, Jordan Reed, Dev Shah Aug 2026

Optimization Of Engine, Jordan Reed, Dev Shah

Discovery Day - Daytona Beach

A matrix-based framework for modeling and optimizing fluid and gas in feed systems to pressurize for propulsion applications using advanced linear algebra techniques will be used in this project. The governing equations are derived from conservation of mass, momentum, and energy and are formulated in state space form. This enables the system to be expressed as a set of coupled linear differential equations. These equations are assembled into structured system matrices that show the interactions between pressure, flow rate, and component dynamics. This representation allows for numerical implementation and scalability to complex systems with multiple components. System behavior is analyzed …

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Modeling Seiche Oscillations Using Damped Vibration Differential Equations, Bianca Gerity, Arineh Shahbazi Aug 2026

Modeling Seiche Oscillations Using Damped Vibration Differential Equations, Bianca Gerity, Arineh Shahbazi

Discovery Day - Daytona Beach

A seiche oscillation is a standing wave that oscillates in an enclosed body of water, like a lake or pool. Seiches are caused by strong winds, earthquakes, and rapid atmospheric changes. Seiches are an excellent real-world example of damped harmonic motion. The physics of these unique vibrations can actually be modeled using a second-order differential equation for damped oscillators of the general form mx''+cx'+kx=0, where m represents the mass of the vibrating water column, c represents the energy dissipation due to friction and viscosity, and k represents the force governed by gravity and the basin's geometry. The objective of this …

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Modeling Seiche Oscillations Using Damped Vibration Differential Equations, Sharjeel Malik, Justin Della Aug 2026

Modeling Seiche Oscillations Using Damped Vibration Differential Equations, Sharjeel Malik, Justin Della

Discovery Day - Daytona Beach

Combustion instability in liquid rocket engines is driven by coupling acoustic pressure oscillations and unsteady heat release. To achieve specific desired outcomes, small perturbations can be made to either decay or grow, depending on system dynamics and artificial parameters. Using a linearized eigenvalue framework, where eigenvalues determine growth/decay rates and frequencies, and eigenvectors describe spatial mode shapes and couplings between pressure, velocity, and heat release, a mathematical model can be derived to describe said behavior for a cross-section of the rocket engine. The Rayleigh criterion is used to identify conditions under which energy is added to oscillations, while flame transfer …

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Navier Stokes Pressure Drop Derivation, Brayden Benedetti, Gedaliah Dimbert, Jaden Turobiner Aug 2026

Navier Stokes Pressure Drop Derivation, Brayden Benedetti, Gedaliah Dimbert, Jaden Turobiner

Discovery Day - Daytona Beach

Accurate prediction of pressure losses in propellant and fluid feed systems is essential for reliable design and operation of aerospace and industrial flow networks. This project presents a systematic derivation of a practical pressure drop calculator for a feed system using isopropyl alcohol, beginning from the fundamental conservation laws and culminating in an engineering-level computational model. Starting with the differential form of the Navier–Stokes equations for incompressible flow, the governing equations are simplified through a series of physically justified assumptions, including steady-state flow, negligible body forces, and fully developed internal flow within circular piping. The resulting momentum balance is reduced …

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Application Of Navier Stokes In Cfd, Hayden Kerkhoff, Gavin Palmer, Garret Seckinger Aug 2026

Application Of Navier Stokes In Cfd, Hayden Kerkhoff, Gavin Palmer, Garret Seckinger

Discovery Day - Daytona Beach

This project investigates the use of 2-Dimensional Computational Fluid Dynamics (CFD) to analyze aerodynamic behavior, then compare data with the numerical solution of the Navier–Stokes equations run by MATLAB. By leveraging open‑source and possible industry CFD platforms—including OpenFOAM and commercial solvers such as ANSYS Fluent and Inventor Professional—the study evaluates how computational methods simulate, optimize, and predict key aerodynamic quantities such as lift, drag, stall angle, and Reynolds number.   The project focuses on modeling an airflow over specific parameters, such as different angles of attacks and ISA Atmospheric Conditions. Parametric variations in density, angle of attack, chord length, and temperature …

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Mechanical Vibrations And Damping, Axon Deadrick, Will Standish, Tanay Agarwal Aug 2026

Mechanical Vibrations And Damping, Axon Deadrick, Will Standish, Tanay Agarwal

Discovery Day - Daytona Beach

Mechanical vibrations occur in many engineering systems and can be described using second-order differential equations. In this project, the motion of vibrating systems is studied using the mass–spring model. The focus is on three types of oscillations: free vibrations, dampened vibrations, and forced oscillations. Free vibration describes how a system moves when it is displaced and then released without any external force. Damped vibration includes effects such as friction or resistance that cause the motion to gradually decrease over time. Forced oscillations occur when an external force acts on the system and continuously drives the motion. This project also examines …

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Numerical Modeling Of Badminton Shuttlecock Trajectories, Lola G. Torres, Cassandra Pumphrey, Jadyn Peterson, Domenic Barsotti Aug 2026

Numerical Modeling Of Badminton Shuttlecock Trajectories, Lola G. Torres, Cassandra Pumphrey, Jadyn Peterson, Domenic Barsotti

Discovery Day - Daytona Beach

The Trajectory of a badminton Shuttlecock can vary significantly when compared to a classic projectile motion, primarily due to aerodynamic drag. This project aims to model the flight of the shuttlecock using Newton's second law for gravitational and drag related forces, resulting in a nonlinear system of a first order differential equation. The given parameters include the shuttlecock mass, cross-sectional area, air density, as well as the drag coefficient, determining the overall magnitude of the drag force. The resulting initial value problem is solved numerically using a multitude of Runge_Kutta methods to compare the accuracy and stability across different computational …

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Motion With Air Resistance, Gauge Mccain, Jacob Bealefeld, Francesca Wise Aug 2026

Motion With Air Resistance, Gauge Mccain, Jacob Bealefeld, Francesca Wise

Discovery Day - Daytona Beach

The motion of objects moving through air is influenced not only by gravity but also by air resistance, which affects the speed and acceleration of the object over time. This project examines the motion of a falling object by modeling it with an ordinary differential equation that accounts for both gravitational force and a resistive drag force proportional to velocity. Using Newton’s Second Law, a first-order differential equation is derived to describe how the velocity of the object changes as it falls. The solution of this equation demonstrates how the velocity increases initially and gradually approaches a constant value known …

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A Differential Equation Approach To Heat Flow In A Thin Rod, Alexandria Krol, David Cardona, Collin Petrie Aug 2026

A Differential Equation Approach To Heat Flow In A Thin Rod, Alexandria Krol, David Cardona, Collin Petrie

Discovery Day - Daytona Beach

A Differential Equation Approach to Heat Flow in a Thin Rod examines how differential equations can be used to model and understand heat conduction in a fundamental physical system. Heat transfer in solids is a key concept in physics and engineering, particularly in systems where temperature changes over time. A thin rod provides a useful one-dimensional model for studying how heat moves through a material and how temperature varies along the rod as time passes. The primary objective is to develop a mathematical description of this process using differential equations. The analysis begins with physical principles such as conservation of …

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Mechanical Vibrations And Damping – Structural Analysis, Kelsey Hunsicker, Sarah Kraus, Sophia Muller Martinelli De Souza Aug 2026

Mechanical Vibrations And Damping – Structural Analysis, Kelsey Hunsicker, Sarah Kraus, Sophia Muller Martinelli De Souza

Discovery Day - Daytona Beach

Mechanical Vibrations are crucial in understanding and structural analysis of engineering systems such as bridges and airplane wings. If not considered, these vibrations can lead to structural fatigue or failure. By using differential equations, structural vibrations will be examined. Researching the different kinds of vibrations and damping will help to find the vibration behavior of the system. For example, a mass-spring damper system will use second-order linear differential equations. The systems model can be shown to be underdamped, overdamped, or critically damped. These will compare the amplitudes and oscillation differences between the systems by using computational code. Analyzing these differences …

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Numerical Investigation Of The Nonlinear Simple Pendulum And The Dependence Of Oscillation Period On Initial Angle, Kelly Wold, Aidan Hart, Patrick Gilliam Aug 2026

Numerical Investigation Of The Nonlinear Simple Pendulum And The Dependence Of Oscillation Period On Initial Angle, Kelly Wold, Aidan Hart, Patrick Gilliam

Discovery Day - Daytona Beach

Numerical Investigation of the Nonlinear Simple Pendulum and the Dependence of Oscillation Period on Initial Angle examines how the oscillation period of a simple pendulum varies with initial angular displacement and evaluates the accuracy of numerical methods in capturing this behavior. In classical treatments, the small-angle approximation simplifies the governing differential equation and predicts a constant period independent of amplitude; however, this assumption breaks down for larger angles, where the system exhibits nonlinear dynamics. The objective of this project is to model the full nonlinear equation of motion and quantify how the period depends on initial conditions. To achieve this, …

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