Kinematics: knowledge representation

December 11th, 2011

This headline is entirely devoted to solving problems. It contains two categories – the training examples for testing for control of the most common relationships between the physical quantities, as well as a workshop on the task solutions. 

Items presented on the workshop website are part of the author’s learning system.

The semantic network for knowledge representation of kinematics

From the beginning of the 70th of the 20th century, our society has been named “information society” due to the appearance of information technologies.

The development of information technologies is determined by such factors: the construction of personal computers, the development of versatile operation systems for computers, the creation and development of fiber optic communication, and the storage of data devices with a high capacity.

The appearance of computers in the pedagogical system brings two new conceptions: the graph and the frame.

Flowcharts of computer programs are graphs. For the first time the concept of “graph” has been applied by the Swiss mathematician Leonhard Euler to solve the problem of the bridges of Konigsberg city.

The concept of the “frame” was proposed by M. Minsky in 1974. According to M. Minsky frame is the cognitive scheme that can be filled out by various information. The frame can be expressed in a graphic or a verbal form. The frame in a verbal form consists of slots that have a name and a value. The frame in a graphic form consists of vertices and arcs. The vertices have the values and the arcs that express the relationship between vertices. The frame that is unfilled by information (vertices and arcs) is called a “proto-frame”, the filled frame is called an “exo-frame”.The frames have become the main link in the creation of programs called “expert systems”. Expert systems use the relationship of “is”, “has”, and “there”. The graphs that present the information in expert systems are called “semantic networks”.

Let us use the new type of relationships called “differentiation” and “integration”. Let us build the proto frame using these relationships: if B1 and B2 are the values, D1 is the operator of differentiation and D2 is the operator of integration (fig. 1).


 Fig. 1. The proto-frame for knowledge representation of kinematics.

Let us fill out the vertices and arcs of the proto-frame with information from kinematics: linear and circular motion. We receive the exo-frames (fig. 2).


Fig. 2. The exo-frames in kinematics show the relations between the displacements, velocities, and accelerations defined for the linear and circular motions.

The exo-frames use the operator of differentiation and the operator of integration. The action of these operators can be demonstrated for the displacement  and the velocity  with the use of equations (1, 2):


Let’s connect the vertices which have equal values; the values which are different from a coefficient we can connect by ribs. We receive the semantic net for knowledge representation of kinematics (fig. 3).


Fig. 3. The semantic network of kinematics knowledge representation.

This semantic net allows us to solve and construct the tasks in a way of route search.


Task 1. Find  s(t) for the body on the filament wound on the block with the radius R, if the equation of the block rotation is: φ(t) = A + Bt2

Buy the solution for 3 euros:

(According to materials of the author’s article: Shvets V.D. Cognitive Aspects of the Frame Applications in the Education // Kognitywistyka I media w edukacji. – 2015. -  number 2. – P. 73-86. Copyright reserved by certificate Number 45754 from 25.09.2012. More information can be found at

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