Classical Mechanics

General Information
Course title: Classical Mechanics
Course catalog description: Advanced classical mechanics, including the variational principles, Lagrange and Hamilton mechanics, and linear and nonlinear systems.
Course registration number: PHYS 6220/7220
Course credits: 3
Semester offered: Fall 2023
Class time: MWF 10:00 a.m. – 10:55 a.m.
First class: Monday, 28th August 2023
Last class: Friday, 08th December 2023
Final Examination: From 10:15 a.m. through 12:15 p.m., Monday, 11th December 2023 as per university examination schedule.
Holidays: 04 September, 16 and 17 October, 10, 22-24 November; as per the university Academic Calendar.
Classroom: This class is remote synchronous. McMaster Hall Room 4012 (MH 4012) is available in case you need a quiet room during classtimes. All classes will meet at the following link: Download information for Webex may be found at: During online instruction, students must keep their videos on with an UToledo background found at The student's display name should be in the following format: "First Last". Examples: "John Doe" and "Jane Doe".

Class Website:
Prerequisites: Permission of Instructor
Course Text: Classical Mechanics, 3rd Edition, Herbert Goldstein, Charles Poole and John Safko, Addison Wesley, ISBN 0-201-65702-3
An errata index to the text has been compiled.
Other References: Classical Dynamics of Particles and Systems, Marion and Thornton
Analytical Mechanics, Fowles
Mechanics, Landau and Lifshitz
Schaum's Outline of Theory and Problems of Lagrangian Dynamics, Dare A. Wells, McGraw Hill, ISBN 07-069258-0

About Instructor
Instructor: Sanjay V. Khare
Title: Professor
Office: MH 5010
Phone: 419-530-2292
Email: sanjay (dot) khare (at)
Office Hours: by appointment

About Grading
Excused absence policy to be followed according to the University guidelines.
The percentage cutoffs to assign letter grades will be determined by the instructor at the end of the semester.
Grading Scheme:
Homework: 20%
In-Class Presentations: 20%
First Exam: 20%
Second Exam: 20%
Final Exam: 20%

We will cover parts of Chapters 1-6, 8, and 9 of the text. We will not cover all chapters in their entirety. Some sections will be omitted. Depending on student interests some modifications in the syllabus may be accommodated. The detailed course agenda is shown here.

Student Learning Objectives
(i) Students will be able to understand the motion of particles and bodies under the influence of various types of forces such as gravitational, frictional, electromagnetic, elastic, and contact forces.
(ii) Students will be able to understand the derivation, modification, and application of the variational approaches to mechanics such as the Lagrangian and Hamiltonian methods.
(iii) Students will gain expertise in the formulation and solution of problems involving forces listed in (i) and the techniques in (ii).

Tips to Succeed in this Course
(i) Understand the derivations so that you can derive them yourself or explain them to someone else logically. Just memorizing them is not of much value.
(ii) Modify the assumptions in the derivations to come up with entirely new derivations. Also, try adding more assumptions to standard derivations from the text to derive results for new special cases.
(iii) Solve lots of problems from the text or other sources.
(iv) Make up your own problems which are totally new or are modifications of those you solve. Then solve these problems.
(v) Discuss course material with fellow students and/or senior students.

Expectations from Students
(i) Look at the class web-site at least once either before or after each class for the latest updates.
(ii) Submit homework in class at the beginning of the class when due. On every homework assignment on the top front page, list student's name, identification number, course number, and homework number. Each homework assignment should be stapled together or put in a binder. Loose pages are not acceptable.
(iii) Read relevant sections from the text that will be covered in the class. These will be announced in the preceding class.
(iv) If you are late to class or decide to leave early do so discretely so as not to disturb others. Seat yourself towards the back exit door if your early exit is known in advance or when you enter late.
(v) Turn off sound on watches, cell phones, pagers, tablets, laptops and all other electronic devices while in class.
(vi) In general, maintain an environment conducive to learning in the classroom.
(vii) Complete all homework and examinations honestly.
(viii) Please do not bring any food or drinks inside the classroom.
(ix) If you have any disabilities hindering your ability to follow any of these rules and/or needing any special considerations bring them to the attention of the instructor immediately. Contact the Student Disability Services Office immediately. See Relevant University Policies below.

Relevant University Policies

Graduate Policies
Graduate Policies:

Policy Statement on Non-Discrimination on the Basis of Disability (ADA)
The University is an equal opportunity educational institution. Please read The University's Policy Statement on Nondiscrimination on the Basis of Disability Americans with Disability Act Compliance. Students can find this policy along with other university policies listed by audience on the University Policy webpage.

Academic Acomodations
The University of Toledo embraces the inclusion of students with disabilities. We are committed to ensuring equal opportunity and seamless access for full participation in all courses. For students who have an Accommodations Memo from the Office of Accessibility and Disability Resources, I invite you to correspond with me as soon as possible so that we can communicate confidentially about implementing accommodations in this course.
For students who have not established accommodations with the Office of Accessibility and Disability Resources and are experiencing disability access barriers or are interested in a referral to health care resources for a potential disability, please connect with the office by calling 419-530-4981 or sending an email to

Academic and Support Services
Please follow this link to view a comprehensive list of Student Academic and Support Services available to you as a student.

Safety and Health Services
Please use the following link to view a comprehensive list of Campus Health and Safety Services available to you as a student and click here for information on the Office of Public Safety.

Basic Needs
Students facing food insecurity may contact the Dean of Students for support (Student Union 2509, 419-530-8852,

Diversity and Inclusion Statement
In this class, we will work together to develop a learning community that is inclusive and respectful. Our diversity may be reflected by differences in race, culture, age, religion, sexual orientation, gender identity/expression, socioeconomic background, and a myriad of other social identities and life experiences. We will encourage and appreciate expressions of different ideas, opinions, and beliefs so that conversations and interactions that could potentially be divisive turn, instead, into opportunities for intellectual and personal development. See Office of Diversity, Equity and Inclusion.

Special Course Expectations During COVID-19

Maintaining a safe campus during the ongoing COVID-19 pandemic remains a top priority. UToledo continues to follow the guidance of the U.S. Centers for Disease Control and Prevention and Ohio Department of Health to keep our campus safe.

The University of Toledo has a missed class policy. It is important that students and instructors discuss attendance requirements for the course. Anyone with a temperature at or above 100.0 degrees Fahrenheit or who is experiencing symptoms consistent with COVID-19 should not come to campus and do a self-administered COVID test or contact their primary care physician or the Main Campus Health Center at 419.530.3451 or Health Science Campus Student Health and Wellness Center at 419.383.5000 to get tested and treated. Free self-administered COVID tests are available at various locations across both campuses including, many residence halls at the main desk, both Rec. Centers, and the Student Affairs Office in the Student Union. For more information on the symptoms of COVID-19, please go to

COVID-19 testing for sick students is also available on both Main Campus and Health Science Campus. On Main Campus, no appointment is needed. Symptomatic students should go to the door to the left of the main entrance and ring the doorbell or call 419.530.3451. You will be immediately let into the sick area for COVID testing. On the Health Science Campus, symptomatic COVID testing is done at the Comprehensive Care Center on Glendale Ave. You must call 419.383.4545 for an appointment.

Absences due to COVID-19 quarantine or isolation requirements are considered excused absences. Students should notify their instructors and follow the protocols summarized in this document on Navigating COVID-Related Course Concerns.

In the event that you have tested positive for COVID-19 or have been diagnosed as a probable case, please review the CDC guidance on self-isolation and symptom monitoring, and report the disclosure to the Division of Student Affairs by emailing or by connecting with their on-call representative at 419.343.9946. Disclosure is voluntary and will only be shared on a need to know basis with staff such as in the Office of Student Advocacy and Support, The Office of Residence Life, and/or the Office of Accessibility and Disability Resources to coordinate supportive measures or to assist the student as needed.

Face Coverings
Face coverings are currently not required while on campus but students should feel free to wear them. The health experts on campus will continue to monitor the situation and may make changes to this policy as determined by CDC and County Health Department guidelines as infection rates fluctuate if necessary to maintain campus safety.

Doctors and other health care professionals agree that the best way to protect ourselves and each other is to get vaccinated. Case data clearly show that vaccines remain highly effective at preventing serious illness from COVID, including the highly contagious delta variant. If you have not yet received your COVID vaccine, the University encourages you do so as soon as possible. No appointment is needed to get the shot at the UTMC Outpatient Pharmacy, University Health Clinic or Main Campus Pharmacy. Once you receive the COVID vaccination, please register on the COVID Vaccine Registry site at:

Special Notes
It is important to note, that based on the unpredictability of the COVID-19 virus, things can change at any time. So please be patient and understanding as we move through the semester. Please refer to on a regular basis for updates to current requirements or mandates. I also ask that you keep me informed of concerns you may have about class, completing course work/assignments timely and/or health concerns related to COVID.


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