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We consider random walks indexed by arbitrary finite random or deterministic trees. We derive a simple sufficient criterion which ensures that the maximal displacement of the tree-indexed random walk is determined by a single large jump.…
A simple mechanical problem is considered which we believe will help students to familiarize some concepts of mechanics of variable mass systems. Meanwhile they can even learn some thrilling physics of bungee jumping.
We clarify and generalize the ant on a rubber rope paradox, which is a mathematical puzzle with a solution that appears counterintuitive. In this paper, we show that the ant can still reach the end of the rope even if we consider the step…
The inner movement of a trebuchet with swinging counterweight was measured inside a laboratory by the use of rotation sensors to determine angular coordinates for beam, counterweight and sling. Data collection was started before the…
We present a robotic table tennis platform that achieves a variety of hit styles and ball-spins with high precision, power, and consistency. This is enabled by a custom lightweight, high-torque, low rotor inertia, five degree-of-freedom arm…
Previous work has presented both a theoretical foundation for designing terrain park jumps that control landing impact and computer software to accomplish this task. US ski resorts have been reluctant to adopt this more engineered approach…
The heavy-load legged robot has strong load carrying capacity and can adapt to various unstructured terrains. But the large weight results in higher requirements for motion stability and environmental perception ability. In order to utilize…
Jumping is an efficient locomotion strategy to traverse cluttered, uneven, or unstable environments in nature, yet replicating continuous, autonomous leaping in soft robots remains challenging due to limited energy storage and reliance on…
A driven pendulum with vertical oscillations of pendulum support (Kapitza pendulum) possesses a number of unusual properties and is a popular object of both analytical and numerical studies. Although some spectacular results can be…
Jumping and hopping locomotion are efficient means of traversing unstructured rugged terrain with the former being the focus of roboticists; a focus that has recently been changing. This focus has led to significant performance and…
The motion of weights attached to a chain or string moving on a frictionless pulley is a classic problem of introductory physics used to understand the relationship between force and acceleration. Here, we consider the dynamics of the chain…
We show that the vertex-reinforced jump process on the $d$-dimensional lattice with long-range jumps is transient in any dimension $d$ as long as the initial weights do not decay too fast. The main ingredients in the proof are: an analysis…
Quadrupedal animals can perform agile and playful tasks while interacting with real-world objects. For instance, a trained dog can track and catch a flying frisbee before it touches the ground, while a cat left alone at home may leap to…
The Ping Pong gun or Ping Pong bazooka has been a popular and compelling tool for physics education. However, the design necessarily means the ball emerges at subsonic speed. The design has been modified to include a pressure chamber and a…
In this article, we study the behaviour of a looped string launched in ambient air using motorised wheels. We show that the loop, once it reaches its stationary state, is either in the pulley or the air-lifted state. The transition between…
Snake robots have been studied for decades with the aim of achieving biological snakes' fluent locomotion. Yet, as of today, their locomotion remains far from that of the biological snakes. Our recent study suggested that snake locomotion…
The looping pendulum is a simple physical system consisting of two masses connected by a string that passes over a rod. We derive equations of motion for the looping pendulum using Newtonian mechanics, and show that these equations can be…
The rotating saddle not only is an interesting system that is able to trap a ball near its saddle point, but can also intuitively illustrate the operating principles of quadrupole ion traps in modern physics. Unlike the conventional models…
In this work, we examine the whip dynamics in a freely falling chain. We consider an inextensible chain with free ends in the presence of gravity hanging from a fixed pulley. If the configuration is unbalanced, the chain begins to…
As robot make their way out of factories into human environments, outer space, and beyond, they require the skill to manipulate their environment in multifarious, unforeseeable circumstances. With this regard, pushing is an essential motion…