Mathematics Branches, Topics, and Sub-Topics

A structured visual guide to the major mathematical areas and their relationships.

Search by code, branch, topic, subtopic, or a keyword from the descriptions.

70Bxx Kinematics

This subtopic introduces the core ideas in kinematics, including foundational concepts, standard methods, and the main questions used to organize the area. Typical uses include building mathematical background, framing related research problems, and supporting applications in neighboring fields where these concepts provide useful structure.

Specific topics

70B05 Kinematics of a particle

Overview

This topic studies the geometry of motion for a particle, including trajectories, velocity, acceleration, and coordinate descriptions in inertial and non-inertial frames. It is a foundational part of mechanics and underlies many later treatments of constrained and rigid-body motion.

Related Wikipedia Page

Kinematics (Wikipedia)

Useful Links

Key Ideas

  • Position, velocity, and acceleration as time-dependent quantities
  • Curvilinear coordinates and frame-dependent descriptions
  • Trajectory analysis and relative motion

Typical Uses

Used to describe and analyze the motion of particles in mechanics, robotics, and engineering dynamics.

Applications

  • Mechanics education
  • Robotics and motion planning
  • Trajectory analysis in physics and engineering

References

Recommended Textbooks

70B10 Kinematics of a rigid body

Overview

This topic examines the motion of rigid bodies, including angular velocity, rotation matrices, Euler angles, and the relation between body-fixed and space-fixed descriptions. It provides the geometric language for rigid-body dynamics and robotics.

Related Wikipedia Page

Rigid body (Wikipedia)

Useful Links

Key Ideas

  • Angular velocity and instantaneous rotation axes
  • Rotation representations and coordinate transformations
  • Kinematic constraints for rigid-body motion

Typical Uses

Used in robotics, aerospace, and mechanical engineering to describe body motion and orientation.

Applications

  • Robotic manipulators
  • Vehicle and spacecraft attitude
  • Mechanical linkage design

References

Recommended Textbooks

70B15 Mechanisms, robots

Overview

This topic studies the design and analysis of linkages, actuators, and robotic systems as constrained mechanical devices. It combines geometry, kinematics, and control ideas to model how machines move and interact with their environments.

Related Wikipedia Page

Robot (Wikipedia)

Useful Links

Key Ideas

  • Linkage geometry and mobility
  • Forward and inverse kinematics
  • Actuation and task-space motion planning

Typical Uses

Used in robotic design, manipulator analysis, and the synthesis of mechanical devices with prescribed motion.

Applications

  • Industrial robotics
  • Medical devices
  • Automated manufacturing

References

Recommended Textbooks