In my latest post, I explore the work-energy principle, beginning with Euler's first law, where the sum of external forces acting on a body relates to its mass and acceleration. By taking the scalar product of this force with the velocity of the body's center of mass and integrating over time, I show how the change in kinetic energy directly links to the work done by external forces. Work and kinetic energy emerge as scalar quantities, with work's sign depending on the force direction relative to displacement, while kinetic energy always remains non-negative. This principle offers insight into understanding energy transfer in physical systems.
To enhance the readability and authenticity of ancient Greek and Latin texts on my website, I integrated the Cardo font, a specialized Unicode font catering to classical languages. This setup allows me to display a wide range of diacritics, symbols, and characters integral to classical texts. By applying custom CSS classes, I tailored specific sections to showcase classical scripts with translations side by side, maintaining clarity and aesthetic appeal across all devices. This approach improves user experience for those engaging with scholarly content and highlights the richness of ancient manuscripts within a modern digital presentation.
In my recent exploration of dynamics, I investigate how combining the Free Body Diagram (FBD) with a Kinetic Diagram (KD) enables precise dynamic analysis of bodies in motion. While FBD alone suffices in statics by balancing external forces, it's inadequate for dynamics, where inertia and acceleration are central. The KD complements the FBD by accounting for inertial forces, letting me calculate a body's resistance to motion changes. As example for a particle on a curved surface, the equilibrium condition requires integrating normal and tangential force components to ensure the particle stays on the path.
In this blog post, I explore the essential aspects of kinetics, a branch of mechanics focusing on the forces and torques responsible for object motion. Unlike kinematics, which simply describes motion, kinetics examines the causes behind changes in velocity and acceleration. By analyzing Newton's laws, the dynamics of systems of particles, and continuous mass distributions, I uncover how these principles are applied to force-driven motion. With practical applications across engineering and physics, this insight into force interactions provides valuable tools for problem-solving in dynamic systems, especially when addressing mass, force, and energy interactions without the influence of relativistic effects.
In this blog post, I examine the different coordinate systems that enable the analysis of curvilinear motion, focusing on Cartesian, cylindrical, spherical, and intrinsic coordinate systems. Beginning with Cartesian coordinates, where orthonormal vectors remain fixed, I progress to cylindrical and spherical systems, which offer insights into curvilinear motion through position-dependent unit vectors. For more complex motions, I use the tangential and normal coordinate systems, also known as the Frenet-Serret framework, to describe path-based motion.
In this blog post, I introduce kinematics, a branch of mechanics focused on describing motion without regard to the forces causing it. I explore how parameters such as position, velocity, and acceleration can be used to analyze trajectories, helping me predict the motion of particles and rigid bodies. This article covers key concepts like vector time derivatives in various reference frames, particle kinematics, and rectilinear motion, providing essential tools for solving problems involving straight-line and general motion. Aimed at expanding my understanding of dynamic motion analysis, this discussion serves as an entry point into deeper dynamics studies.
In this blog post, I explain my approach to handling cache updates in HTML5 applications that support offline access. While caching assets with a Service Worker enables offline functionality, it often prevents automatic updates when new versions are available. To solve this, I developed a method that uses a version check, prompting the Service Worker to refresh cached files when updates are detected. I also notify the user to reload the page once updates are in place, ensuring they receive the latest version. This approach maintains offline access while ensuring that users access the most up-to-date content whenever possible.
In my latest post, I explore the implementation of localization in HTML5 applications using i18next, a robust internationalization framework for JavaScript. I explain how to integrate language detection and dynamic content updates to create a user-friendly multilingual experience. With a structured approach, I demonstrate initializing i18next, managing translation resources, and ensuring adaptable text updates based on language settings. Additionally, I cover strategies for maintaining modular translation files, avoiding hardcoded text, and the importance of consistent testing across languages. This guide offers practical insights and code examples for developing accessible, globally-oriented applications.
I recently built a Color Picker, a practical web tool to explore HTML, CSS, and JavaScript, while learning about the intricacies of interactive web design. This color picker includes essential features like a hexagonal grid for color selection, real-time display updates, and an option to toggle between color and grayscale modes. Through CSS styling, I structured the picker to be visually engaging, using properties like `clip-path` for hexagonal cells, and JavaScript to handle color conversions and event-based user interactions. This tool combines intuitive UI design with technical precision, and I share my approach here for those interested in building interactive web elements.
I recently built a Color Picker, a practical web tool to explore HTML, CSS, and JavaScript, while learning about the intricacies of interactive web design. This color picker includes essential features like a hexagonal grid for color selection, real-time display updates, and an option to toggle between color and grayscale modes. Through CSS styling, I structured the picker to be visually engaging, using properties like `clip-path` for hexagonal cells, and JavaScript to handle color conversions and event-based user interactions. This tool combines intuitive UI design with technical precision, and I share my approach here for those interested in building interactive web elements.
In this blog post, I'll walk you through the creation of a responsive calculator app using HTML, CSS, and JavaScript. The project covers the structure, styling, and interactive functionality of a basic calculator, allowing users to perform essential arithmetic operations. By structuring the calculator layout in HTML, enhancing appearance with CSS, and implementing interactivity through JavaScript, this project serves as a solid practice in web development skills. The app's layout is fully responsive, adapting smoothly to different screen sizes, and includes custom JavaScript functions to handle inputs, operations, and calculations efficiently.
In this post, I focus on using service workers to enhance my HTML5 app's offline capabilities and performance. Service workers act as intermediaries between my app and the network, enabling caching strategies that store essential resources locally. I walk through the registration process, detailing inline scripting requirements for security and controlling the scope of my service worker. I also provide a practical service worker example, designed to cache assets like HTML, CSS, JavaScript, and app icons for fast offline access. This approach ensures that my application remains responsive even under poor network conditions, with simplified cache versioning for maintenance.
Packaging an HTML5 application for mobile requires a precise setup to achieve a consistent and high-performing user experience. In this post, I explore the critical role of the manifest file in defining app metadata, icons, theme colors, and the start URL, allowing my application to present a seamless, native-like experience on mobile devices. Additionally, I implement service workers to enhance app performance through intelligent caching strategies, minimizing load times and optimizing offline functionality. This combination of manifest and service workers represents a powerful approach for developers aiming to create user-friendly and robust mobile web applications.
Adding a unique touch to a webpage can elevate user experience, and an HTML5 canvas element can do just that. In this post, I walk through creating a dynamic banner using HTML, CSS, and JavaScript, replacing a static image with an interactive asteroid simulation. The simulation features a starship that follows the mouse and avoids obstacles, making for an engaging, immersive visual. I'll cover setting up the canvas, coding asteroid and starship animations, and implementing mouse-tracking for responsive, screen-specific designs that work seamlessly on both desktop and mobile.
In this final part of my GPT model implementation, I focus on integrating model introspection to better understand the architecture and parameters. To monitor training, I visualized the loss using both simple and exponential moving averages, smoothing the trends and making it easier to evaluate performance.