It was my 5 th year of Muay Thai training. I had come to a point where I had really plateaued. I was putting in the hours…I was even training in Thailand when I had these thoughts of quitting. Instantly, from the moment I started training, he saw a fundamental piece missing in my training for all of these years…I had dead footwork.
Like a drill sergeant, he trained me to have perfect form for every movement to undo bad habit. It was a long road, but as I continued training with him, patterns of movement among the form started to arise.
I came into it to share the journey of personal transformation with others. I had a story to tell and I wanted to tell it through teaching Muay Thai. Through years of teaching people in this manner, I continued tinkering with the principles and refined it down to core ones…that would allow me to keep training. And I want to share them with you so hopefully you can make these discoveries within your journey.
Muay Thai can seem complex at first. But like anything…break it down into small of enough chunks, the movements become simple and masterable for anyone.
And this is what these 7 principles are. The first four are about the basic movements of the feet, hips and lower back.
The most important part of Muay Thai is the stance…. The word stance…I hate that word. Because it shrouds the meaning behind it. What is a stance really though? So the knees stay bent…the elbows bent, the hips and shoulders loose…so that when we need power…we can snap the bones. By curling the body forward, we create a looseness in the torso…opposite of the squat. In a recent scientific analysis, we found that the shrimp is driven primarily by the abs, curled forward…Minimal muscle activation anywhere else but the abs.
That goes for the leg, the arms, the lower back…Nothing. The abs were the only thing active. The key take away is that the weight is to the front. If you find tension in your hips and shoulders…relax it. Allow the abs to curl your body forward like a crunch.
In Muay Thai, all strikes, movements are done with the entire body moving to generate force…for strikes, for footwork, for blocks. The majority of our weight is centered around our trunk…our hips, torso…and shoulder….
How we shift our weight through our feet is different from how we shift our weight in our torso. At the feet. In the pic to the right, I emphasize that like an ice skater cutting into the ground on one foot, we cut into the ground with the lead foot for the cross. But what about up top…the trunk?
The hip. Only after we secure the foot placement do we shift our weight to that side. And the first line of action after our foot placement is driving our hip forward over it, since the foot is connected to the hip. Whenever I teach people, I always start by training them on this principle first. This is where the weight is on the boot…primarily through the big toe…and nugget…down to the heel.
Basics of Engineering Mechanics: Introduction
How does this work? And securing this, is the first part of that BOOT. Principle 4 — Driving the hip forward after securing the foot with the boot.For reference purposes and to help focus discussions on Physics Forums in interpretation questions on the real issues, there is a need for fixing the common ground.
There is no consensus about the interpretation of quantum mechanics, and — not surprisingly — there is disagreement even among the mentors and science advisors here on Physics Forums. I slightly expanded the final version and added headings and links to make it suitable as an Insight article.
A revised version of this article is published as Section 1. The basic rules reflect what is almost generally taught as the basics in quantum physics courses around the world. Often they are stated in terms of axioms or postulates, but this is not essential for their practical validity. In some interpretations, some of these rules are not considered fundamental rules but only valid as empirical or effective rules for practical purposes.
These rules describe the basis of the quantum formalism and are found in almost all introductory quantum mechanics textbooks, among them: Basdevant ; Cohen-Tannoudji, Diu and Laloe ; Dirac; Gasiorowicz ; Greiner ; Griffiths and Schroeter ; Landau and Lifshitz; Liboff ; McIntyre ; Messiah ; Peebles ; Rae and Napolitano ; Sakurai ; Shankar ; Weinberg These generalizations are necessary to be able to apply quantum mechanics to all situations encountered in practice.
The basic rules are carefully formulated so that they are correct as they stand and at the same time fully compatible with these generalizations.
When stating the rules, italic text corresponds to the physical systems, its preparation, measurement, measured values etc.
Mixed states are represented by more general non-idempotent Hermitian density operators of trace 1. The evolution according to 3 is therefore also referred to as unitary evolution.
Note that there is no direct conflict with the unitary evolution in 3 since during a measurement, a system is never isolated. In other cases, the prepared state may be quite different. See the discussion in Landau and Lifschitz, Vol. III, Section 7. The most general kind of quantum measurement and the resulting prepared state is described by so-called positive operator valued measures POVM s.
Not further discussing the foundations of quantum mechanics beyond this is called shut-up-and-calculate. It is the mode of working sufficient for all who do not want to delve into often highly disputed foundational and partly philosophical problems.
The associated issues are treated in different ways by different interpretations of quantum mechanics. In the Copenhagen Interpretation also called Standard Interpretation or Orthodox Interpretation; terminology and interpretation details varythe above rules are simply operational rules that work in practice.
The state vector is a tool that one uses to calculate the probabilities of measurement outcomes, and one is agnostic about whether the state vector represents any object that exists in reality. Rules 6 and 7 apply only when a measurement has occurred. Thus unlike in classical physics, it is not enough to specify the initial conditions of the state, and let the state evolve.
One must also specify when a measurement has occurred: Generally, a measurement is understood to have occurred when a definite irreversible, i. However passing a Stern-Gerlach magnet — which in modern terminology is a premeasurement only — is frequently but inaccurately considered to be a measurement, although it is described by a unitary process where even in principle no measurement result becomes available.
A noteworthy aspect of the standard interpretation is that the state vector cannot represent the whole universe, but must exclude an observer or measuring apparatus that decides when a measurement has occurred; this is the so-called Heisenberg cut between the quantum and the classical world.
To date, this has not been a problem in making successful experimental predictions, so practitioners are often satisfied with the quantum formalism and the standard interpretation. However, many have suggested that there is a conceptual problem with the standard interpretation because the whole universe presumably obeys laws of physics. So there should be laws of physics that describe the whole universe, without any need to exclude any observer or measurement apparatus from the quantitative description.
Then one must be able to derive the rules 5 - 7 for measuring subsystems of the universe from the dynamics of the universe. The problem of how to do this is called the measurement problem. A related problem, the problem of the emergence of a classical macroscopic world from the microscopic quantum description, is often considered as essentially solved by decoherence. To solve the measurement problem, other interpretations of the quantum formalism or theories have been proposed.
These alternative interpretations or theories are based on different postulates than those of the standard interpretation, but seek to explain why the standard interpretation has been so successful e. Still other interpretations e. None of the interpretations currently available has been able to solve the measurement problem in a way deemed satisfactory by those interested in the foundations.From the very childhood we have seen footballs bouncing and wheels rolling.
We might have wondered how all these motions happen. These all motions are interaction of different bodies and effect of forces acting on them.
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The branch of science dealing with the effect of forces on bodies is called Mechanics. The principles of Mechanics are exactly applicable to machines, it may be a simple machine such as a liver or bicycle or a machine as complex as an aircraft. When Mechanics is applied in Engineering, design and analysis of mechanisms and machine, it is called as Engineering Mechanics.
When bodies interact and forces act between them there are two possibilities, they may move or they may remain static. The branch of Engineering Mechanics dealing with the motion of bodies is called as Dynamics and the other branch is called as Statics, in which we study balance and equilibrium of bodies.
So complete understanding of these laws is a must. Along with this, as the physical quantities encountered during engineering analyses are mostly vectors, the adequate knowledge of vector algebra is required. This branch of engineering mechanics deals with bodies in equilibrium and are not moving with respect to the frame of reference considered for analysis.
Bodies may be experiencing different forces but the configuration of these forces is such that the resultant force on the system is zero. The unbalanced forces tend to accelerate a body but if net force is zero the body will not accelerate. In addition to accelerating a body forces make bodies rotate. This ability of a force to rotate a body is called as torque or moment of the force. For true static equilibrium the net moment or torque on a body should also be zero along with zero net force.
Statics include force analysis in stationary structures such as trusses, frames and machines at certain stationary positions. Cables and strings in stationary positions in mechanical systems also comes under the purview of statics. The analysis of forces and motion in moving bodies comes in Dynamics. This branch of engineering mechanics is further divided in two branches, kinematics and kinetics.
Kinematics deals with the analysis of motion of bodies without considering the forces causing or associated with these motions. In Kinematics the position, velocity and acceleration of certain points and the members of mechanisms and machines is studied. The kinematic analysis starts with particles and is then extended to rigid bodies. Read Kinematics as applied to the analysis and synthesis of mechanisms and machines.
The forces causing motion in bodies are studied under kinetics. Kinetics include analysis of causal force, impulse and momentum of bodies.To browse Academia. Skip to main content. Log In Sign Up. Basic mechanics Basic principles of statics. Vishal Bahamni. The other main branch — dynamics — deals with m is the product of the mass and the acceleration due moving bodies, such as parts of machines. The point of application must also be specified.
A vector is illustrated by a line, the length of Static determinacy which is proportional to the magnitude on a given scale, If a body is in equilibrium under the action of coplanar and an arrow that shows the direction of the force. In general, three independent unknowns can be determined from Vector addition the three equations.
Note that if applied and reaction The sum of two or more vectors is called the resultant. Such systems of The vectors to be added are arranged in tip-to-tail forces are said to be statically determinate. Where three or more vectors are to be added, they can be arranged in the same manner, and this is Force called a polygon. A line drawn to close the triangle A force is defined as any cause that tends to alter the or polygon from start to finishing point forms the state of rest of a body or its state of uniform motion resultant vector.Michio Kaku: The Universe in a Nutshell (Full Presentation) - Big Think
A force can be defined quantitatively The subtraction of a vector is defined as the addition as the product of the mass of the body that the force is of the corresponding negative vector. Coplanar forces lie in the same plane, whereas non-coplanar forces have to be related to a three-dimensional space and require two items Q of directional data together with the magnitude. The closed triangle or polygon is a graphical expression of the equilibrium of a particle.
This second force, which restores equilibrium, is called the equilibrant. Q When a particle is acted upon by two or more forces, the A equilibrant has to be equal and opposite to the resultant of the system. Thus the equilibrant is the vector drawn closing the vector diagram and connecting the finishing Q point to the starting point.
The force effects along these axes are called vector components and are obtained by reversing the vector addition method.Read this paper on arXiv.
The list of basic axioms of quantum mechanics as it was formulated by von Neumann includes only the mathematical formalism of the Hilbert space and its statistical interpretation. We point out that such an approach is too general to be considered as the foundation of quantum mechanics.
In particular in this approach any finite-dimensional Hilbert space describes a quantum system. I present a list from seven basic postulates of axiomatic quantum mechanics. In particular the list includes the axiom describing spatial properties of quantum system.
These axioms do not admit a nontrivial realization in the finite-dimensional Hilbert space. One suggests that the axiomatic quantum mechanics is consistent with local realism.
Most discussions of foundations and interpretations of quantum mechanics take place around the meaning of probability, measurements, reduction of the state and entanglement. The list of basic axioms of quantum mechanics as it was formulated by von Neumann [ 1 ] includes only general mathematical formalism of the Hilbert space and its statistical interpretation, see also [ 2 ] - [ 6 ].
From this point of view any mathematical proposition on properties of operators in the Hilbert space can be considered as a quantum mechanical result. From our point of view such an approach is too general to be called foundations of quantum mechanics. We have to introduce more structures to treat a mathematical scheme as quantum mechanics.
These remarks are important for practical purposes. If we would agree about the basic axioms of quantum mechanics and if one proves a proposition in this framework then it could be considered as a quantum mechanical result. Otherwise it can be a mathematical result without immediate relevance to quantum theory.
It is known that the correlation function of two spins computed in the four-dimensional Hilbert space does not satisfy the Bell inequalities. However from the previous discussion it should be clear that such a claim is justified only if we agree to treat the four-dimensional Hilbert space as describing a physical quantum mechanical system. In quantum information theory qubit, i.
Let us note however that in fact the finite-dimensional Hilbert space should be considered only as a convenient approximation for a quantum mechanical system and if we want to investigate fundamental properties of quantum mechanics then we have to work in an infinite-dimensional Hilbert space because only there the condition of locality in space and time can be formulated.
There are such problems where we can not reduce the infinite-dimensional Hilbert space to a finite-dimensional subspace. We shall present a list from seven axioms of quantum mechanics.
The axioms are well known from various textbooks but normally they are not combined together. Then, these axioms define an axiomatic quantum mechanical framework. If some proposition is proved in this framework then it could be considered as an assertion in axiomatic quantum mechanics.
Of course, the list of the axioms can be discussed but I feel that if we fix the list it can help to clarify some problems in the foundations of quantum mechanics. For example, as we shall see, the seven axioms do not admit a nontrivial realization in the four-dimensional Hilbert space. This axiomatic framework requires an infinite-dimensional Hilbert space.
In this note it is proposed that the key notion which can help to build a bridge between the abstract formalism of the Hilbert space and the practically useful formalism of quantum mechanics is the notion of the ordinary three-dimensional space.The previous collection of things everyone should know about quantum physics is a little meta-- it's mostly talking up the importance and relevance of the theory, and not so much about the specifics of the theory. Here's a list of essential elements of quantum physics that everyone ought to know, at least in broad outlines:.
Quantum physics tells us that every object in the universe has both particle-like and wave-like properties. It's not that everything is really waves, and just sometimes looks like particles, or that everything is made of particles that sometimes fool us into thinking they're waves. Every object in the universe is a new kind of object-- call it a "quantum particle" that has some characteristics of both particles and waves, but isn't really either.
Quantum particles behave like particles, in that they are discrete and in principle countable. Matter and energy come in discrete chunks, and whether you're trying to locate an atom or detect a photon of light, you will find it in one place, and one place only. Quantum particles also behave like waves, in that they show effects like diffraction and interference. If you send a beam of electrons or a beam of photons through a narrow slit, they will spread out on the far side.
If you send the beam at two closely spaced slits, they will produce a pattern of alternating bright and dark spots on the far side of the slits, as if they were water waves passing through both slits at once and interfering on the other side.
This is true even though each individual particle is detected at a single location, as a particle. The "quantum" in quantum physics refers to the fact that everything in quantum physics comes in discrete amounts. A beam of light can only contain integer numbers of photons-- 1, 2, 3,but never 1. An electron in an atom can only have certain discrete energy values-- No matter what you do, you will only ever detect a quantum system in one of these special allowed states.
When physicists use quantum mechanics to predict the results of an experiment, the only thing they can predict is the probability of detecting each of the possible outcomes.
No matter how careful we are to prepare each electron in exactly the same way, we can never say for definitiviely what the outcome of the experiment will be.
Each new electron is a completely new experiment, and the final outcome is random. Until the moment that the exact state of a quantum particle is measured, that state is indeterminate, and in fact can be thought of as spread out over all the possible outcomes. After a measurement is made, the state of the particle is absolutely determined, and all subsequent measurements on that particle will return produce exactly the same outcome.
The double-slit experiment mentioned above can be thought of as confirmation of this indeterminacy-- until it is finally measured at a single position on the far side of the slits, an electron exists in a superposition of both possible paths.
The interference pattern observed when many electrons are recorded one after another is a direct consequence of the superposition of multiple states. The Quantum Zeno Effect is another example of the effects of quantum measurement: making repeated measurements of a quantum system can prevent it from changing its state.
Between measurements, the system exists in a superposition of two possible states, with the probability of one increasing and the other decreasing. Each measurements puts the system back into a single definite state, and the evolution has to start over. The effects of measurement can be interpreted in a number of different ways-- as the physical "collapse" of a wavefunction, as the splitting of the universe into many parallel worlds, etc.
A quantum particle can and will occupy multiple states right up until the instant that it is measured; after the measurement it is in one and only one state. One of the strangest and most important consequences of quantum mechanics is the idea of "entanglement. You can hold one particle in Princeton and send the other to Paris, and measure them simultaneously, and the outcome of the measurement in Princeton will absolutely and unequivocally determine the outcome of the measurement in Paris, and vice versa.
The correlation between these states cannot possibly be described by any local theory, in which the particles have definite states. These states are indeterminate until the instant that one is measured, at which time the states of both are absolutely determined, no matter how far apart they are.
This has been experimentally confirmed dozens of times over the last thirty years or so, with light and even atoms, and every new experiment has absolutely agreed with the quantum prediction. It must be noted that this does not provide a means of sending signals faster than light-- a measurement in Paris will determine the state of a particle in Princeton, but the outcome of each measurement is completely random. There is no way to manipulate the Parisian particle to produce a specifc result in Princeton.
The correlation between measurements will only be apparent after the fact, when the two sets of results are compared, and that process has to take place at speeds slower than that of light.
A quantum particle moving from point A to point B will take absolutely every possible path from A to B, at the same time. This includes paths that involve highly improbable events like electron-positron pairs appearing out of nowhere, and disappearing again. The full theory of quantum electro-dynamics QED involves contributions from every possible process, even the ridiculously unlikely ones. It's worth emphasizing that this is not some speculative mumbo-jumbo with no real applicability.
A QED prediction of the interaction between an electron and a magnetic field correctly describes the interaction to 14 decimal places.In addressing any problem in continuum or solid mechanicsthree factors must be considered: 1 the Newtonian equations of motionin the more general form recognized by Euler, expressing conservation of linear and angular momentum for finite bodies rather than just for point particlesand the related concept of stressas formalized by Cauchy, 2 the geometry of deformation and thus the expression of strains in terms of gradients in the displacement fieldand 3 the relations between stress and strain that are characteristic of the material in question, as well as of the stress level, temperatureand time scale of the problem considered.
These three considerations suffice for most problems. They must be supplemented, however, for solids undergoing diffusion processes in which one material constituent moves relative to another which may be the case for fluid-infiltrated soils or petroleum reservoir rocks and in cases for which the induction of a temperature field by deformation processes and the related heat transfer cannot be neglected.
These cases require that the following also be considered: 4 equations for conservation of mass of diffusing constituents5 the first law of thermodynamicswhich introduces the concept of heat flux and relates changes in energy to work and heat supply, and 6 relations that express the diffusive fluxes and heat flow in terms of spatial gradients of appropriate chemical potentials and of temperature.
In many important technological devices, electric and magnetic fields affect the stressing, deformation, and motion of matter. Examples are provided by piezoelectric crystals and other ceramics for electric or magnetic actuators and by the coils and supporting structures of powerful electromagnets.
The second law of thermodynamicscombined with the above-mentioned principles, serves to constrain physically allowed relations between stress, strain, and temperature in 3 and also constrains the other types of relations described in 6 and 8 above.
Such expressions, which give the relationships between stress, deformation, and other variables, are commonly referred to as constitutive relations. In general, the stress-strain relations are to be determined by experiment. A variety of mechanical testing machines and geometric configurations of material specimens have been devised to measure them. These allow, in different cases, simple tensile, compressive, or shear stressing, and sometimes combined stressing with several different components of stress, as well as the determination of material response over a range of temperatures, strain rates, and loading histories.
The testing of round bars under tensile stress, with precise measurement of their extension to obtain the strain, is common for metals and for technological ceramics and polymers. For rocks and soils, which generally carry load in compression, the most common test involves a round cylinder that is compressed along its axis, often while being subjected to confining pressure on its curved face.
Frequently, a measurement interpreted by solid mechanics theory is used to determine some of the properties entering stress-strain relations.
For example, measuring the speed of deformation waves or the natural frequencies of vibration of structures can be used to extract the elastic moduli of materials of known mass density, and measurement of indentation hardness of a metal can be used to estimate its plastic shear strength. In some favourable cases, stress-strain relations can be calculated approximately by applying principles of mechanics at the microscale of the material considered.
In a composite materialthe microscale could be regarded as the scale of the separate materials making up the reinforcing fibres and matrix. When their individual stress-strain relations are known from experiment, continuum mechanics principles applied at the scale of the individual constituents can be used to predict the overall stress-strain relations for the composite.
For rubbery polymer materials, made up of long chain molecules that randomly configure themselves into coillike shapes, some aspects of the elastic stress-strain response can be obtained by applying principles of statistical thermodynamics to the partial uncoiling of the array of molecules by imposed strain.
For a single crystallite of an element such as silicon or aluminum or for a simple compound like silicon carbidethe relevant microscale is that of the atomic spacing in the crystals; quantum mechanical principles governing atomic force laws at that scale can be used to estimate elastic constants. In the case of plastic flow processes in metals and in sufficiently hot ceramics, the relevant microscale involves the network of dislocation lines that move within crystals.
These lines shift atom positions relative to one another by one atomic spacing as they move along slip planes. Important features of elastic-plastic and viscoplastic stress-strain relations can be understood by modeling the stress dependence of dislocation generation and motion and the resulting dislocation entanglement and immobilization processes that account for strain hardening.
To examine the mathematical structure of the theory, considerations 1 to 3 above will now be further developed. For this purpose, a continuum model of matter will be used, with no detailed reference to its discrete structure at molecular—or possibly other larger microscopic—scales far below those of the intended application.
Let x denote the position vector of a point in space as measured relative to the origin of a Newtonian reference frame; x has the components x 1x 2x 3 relative to a Cartesian set of axes, which is fixed in the reference frame and denoted as the 1, 2, and 3 axes in Figure 1. Thus, from the microscopic viewpoint, v of the continuum theory is a mass-weighted average velocity.
The linear momentum P and angular momentum H relative to the coordinate origin of the matter instantaneously occupying any volume V of space are then given by summing up the linear and angular momentum vectors of each element of material.
In this discussion attention is limited to situations in which relativistic effects can be ignored. Let F denote the total force and M the total torque, or moment relative to the coordinate originacting instantaneously on the material occupying any arbitrary volume V.
When either F or M vanishes, these equations of motion correspond to conservation of linear or angular momentum. The understanding of such conditions for equilibriumat least in a rudimentary form, long predates Newton. Indeed, Archimedes of Syracuse 3rd century bcthe great Greek mathematician and arguably the first theoretically and experimentally minded physical scientist, understood these equations at least in a nonvectorial form appropriate for systems of parallel forces. This is shown by his treatment of the hydrostatic equilibrium of a partially submerged body and by his establishment of the principle of the lever torques about the fulcrum sum to zero and the concept of centre of gravity.
Mechanics of solids.