ShoulderThe human shoulder is made up of three bones: the clavicle (collarbone), the scapula (shoulder blade), and the humerus (upper arm bone) as well as associated muscles, ligaments and tendons. The articulations between the bones of the shoulder make up the shoulder joints. The shoulder joint, also known as the glenohumeral joint, is the major joint of the shoulder, but can more broadly include the acromioclavicular joint. In human anatomy, the shoulder joint comprises the part of the body where the humerus attaches to the scapula, and the head sits in the glenoid cavity.
Shoulder problemShoulder problems including pain, are one of the more common reasons for physician visits for musculoskeletal symptoms. The shoulder is the most movable joint in the body. However, it is an unstable joint because of the range of motion allowed. This instability increases the likelihood of joint injury, often leading to a degenerative process in which tissues break down and no longer function well. Shoulder pain may be localized or may be referred to areas around the shoulder or down the arm.
Dislocated shoulderA dislocated shoulder is a condition in which the head of the humerus is detached from the shoulder joint. Symptoms include shoulder pain and instability. Complications may include a Bankart lesion, Hill-Sachs lesion, rotator cuff tear, or injury to the axillary nerve. A shoulder dislocation often occurs as a result of a fall onto an outstretched arm or onto the shoulder. Diagnosis is typically based on symptoms and confirmed by X-rays. They are classified as anterior, posterior, inferior, and superior with most being anterior.
Row and column vectorsIn linear algebra, a column vector with m elements is an matrix consisting of a single column of m entries, for example, Similarly, a row vector is a matrix for some n, consisting of a single row of n entries, (Throughout this article, boldface is used for both row and column vectors.) The transpose (indicated by T) of any row vector is a column vector, and the transpose of any column vector is a row vector: and The set of all row vectors with n entries in a given field (such as the real numbers) forms an n-dimensional vector space; similarly, the set of all column vectors with m entries forms an m-dimensional vector space.
Shoulder girdleThe shoulder girdle or pectoral girdle is the set of bones in the appendicular skeleton which connects to the arm on each side. In humans it consists of the clavicle and scapula; in those species with three bones in the shoulder, it consists of the clavicle, scapula, and coracoid. Some mammalian species (such as the dog and the horse) have only the scapula. The pectoral girdles are to the upper limbs as the pelvic girdle is to the lower limbs; the girdles are the parts of the appendicular skeleton that anchor the appendages to the axial skeleton.
Dynamical systems theoryDynamical systems theory is an area of mathematics used to describe the behavior of complex dynamical systems, usually by employing differential equations or difference equations. When differential equations are employed, the theory is called continuous dynamical systems. From a physical point of view, continuous dynamical systems is a generalization of classical mechanics, a generalization where the equations of motion are postulated directly and are not constrained to be Euler–Lagrange equations of a least action principle.
Joint dislocationA joint dislocation, also called luxation, occurs when there is an abnormal separation in the joint, where two or more bones meet. A partial dislocation is referred to as a subluxation. Dislocations are often caused by sudden trauma on the joint like an impact or fall. A joint dislocation can cause damage to the surrounding ligaments, tendons, muscles, and nerves. Dislocations can occur in any major joint (shoulder, knees, etc.) or minor joint (toes, fingers, etc.). The most common joint dislocation is a shoulder dislocation.
Generalized coordinatesIn analytical mechanics, generalized coordinates are a set of parameters used to represent the state of a system in a configuration space. These parameters must uniquely define the configuration of the system relative to a reference state. The generalized velocities are the time derivatives of the generalized coordinates of the system. The adjective "generalized" distinguishes these parameters from the traditional use of the term "coordinate" to refer to Cartesian coordinates.
Row and column spacesIn linear algebra, the column space (also called the range or ) of a matrix A is the span (set of all possible linear combinations) of its column vectors. The column space of a matrix is the or range of the corresponding matrix transformation. Let be a field. The column space of an m × n matrix with components from is a linear subspace of the m-space . The dimension of the column space is called the rank of the matrix and is at most min(m, n). A definition for matrices over a ring is also possible.
Rotator cuffThe rotator cuff is a group of muscles and their tendons that act to stabilize the human shoulder and allow for its extensive range of motion. Of the seven scapulohumeral muscles, four make up the rotator cuff. The four muscles are: supraspinatus muscle infraspinatus muscle teres minor muscle subscapularis muscle. The supraspinatus muscle spreads out in a horizontal band to insert on the superior facet of the greater tubercle of the humerus. The greater tubercle projects as the most lateral structure of the humeral head.
